Your key challenge to my disbursal argument was that "statistically" the movements would average out. Statistically speaking a person with his head on a block of dry ice and his feet in a blast furnace is, on average, feeling just fine

. And yes, I know it is a fallacious argument, as is just about any argument based solely on statistical analysis without accounting for real world issues. As with all uses of statistics things are rarely what they would mathematically appear to be.
If you accelerate in random directions multiple times in a row, that is a behaviour that can be described by statistics, no other model will have a better prediction of where you ultimately will end up, especially if you have a fleet of ships all doing the same thing independently from each other. That is not a fallacious use of statistics.
You can argue that the movement isn't random if a human is making the decisions, and you'd be right, but at the same time, if the person in charge of making the course changes had to think about them, then they wouldn't happen fast enough to evade. And if an AI was in charge of controlling it, then either a pattern emerges or it is truly random and follows the statistical model.
At any range under a minimum of 300,000 km (1 light-second) missing might be a rare thing since dodging would really, as you pointed out, not be useful due to the toothpaste tube effect upon the crew. I would, however, like to point out that in all the tests of the Space Defense System (Reagan's Star Wars Defense) firing at known targets, at known trajectories, there was only 1 hit, and that was a really close in shot. Hitting something at high velocity and range just isn't all that easy -- you have to lead your target by the distance it will travel by the time the energy beam gets there, so I don't have to dodge by all that much -- less than one degree on the trajectory will be a considerable change from projected location at firing.
Comparing humanity's first trials using space weaponry to something an actual space based military uses is not all that useful, that's like comparing a 15th century cannon with modern artillery.
I know you have to shoot at where the target is going to be and not where you see it, that's not a novel concept.
Changing course by one degree or less is all well and good, but the faster you go, the more thrust you need to do that. If you go 1 m/s and apply 1 m/s² of acceleration for 1 s, you have changed course by 45°, if you do the same when you're moving with 2 m/s then you only change your course by 22.5° and in both cases you only end up 1 m from where you would have been if you hadn't applied any thrust. You can therefore disregard your velocity when it comes to evading incoming fire, only your acceleration and the time you have to accelerate matter.
Please don't say that tracking tech will be better, because so will evasive technologies such as stealth and ECM.
Stealth in space is a myth, as long as there is no stealth technology in the game, I will not count it as an option. ECM might or might not work, depending on what the opponent uses to target you. If they can do that with passive sensors, then no, if they use something like radar, then yes. What I was going to say is, that accuracy of such weapons will be much better as well as much better targeting computers and optical scanners.
I agree that missiles and projectiles will be useful only as closer ranged weapons, except for missile tracking making them possible medium ranged and, as you say, PD systems might eat them alive.
I didn't say that, it depends very much on the velocity of projectiles and rate of acceleration the ships can achieve if you can accelerate the projectiles to half the speed of light, you can reliably hit something from quite far away. And if the target can only achieve 1 G of acceleration, your effective range is larger as well. And the faster your missiles are, the fewer you need to overwhelm PD, you still want to shoot large quantities though.
This is about combat in Stallaris. In the game, the larger doomstack wins. Even with differences in technology or ship size (within reason) favoring the smaller stack, ship quantity matters more than quality. This is the issue, not how you array the fleet. There is only one way for ships to behave based on the size of the ship, so there is no tactical control. Of course fleets will concentrate fire, it's programed that way; of course the side with the least ships -- even bigger ones -- will loose just about every time. The issue isn't which of us is right or wrong, the issue is how does this fit any notion of strategy?
I'll repeat it again, this has absolutely nothing to do with Stellaris, this is a characteristic of battles with modern weapons. The relative power of a force compared to another increases by the square of their numbers, a force twice as big as another one is not twice as strong, it's four times as strong. However this only applies to forces involved in combat, not to the total forces one side has. This model of combat has been known since 1916. Tactical control might alter the balance but unless the AI is capable of doing that, it will only benefit the player. It's not combat itself that is the problem, though the all or nothing nature of battles contributes to it, the problem is, that there are no strategic targets besides fleets and to a far lesser degree spaceports. Stellaris is not an RTS game where you micromanage your units in tactical combat situations, it's a grand strategy game, your strategic choices are supposed to be made one abstraction level higher. You don't control individual units (at least you're not supposed to) you control fleets and armies. The problem is, that currently there is only one real strategy in a war, and that is kill the enemy fleet, everything else is a sideshow.
Okay, before I start this... Please teach me how to quote individual sections of text easily. The last time I dissected a post to address individual points it took dozens of minutes to format, so for this I'll just have my responses within your quote in italics.
By selecting the part you want to quote, which should open a little button thingy that says quote|reply, quote adds it to multiquote and reply adds it directly to the comment box.
Not necessarily- a ship would only need maneuvering thrusters and a main engine, or even just a main engine. After all, to change direction all a vessel needs to do is adjust the direction the main engine thrust is propelling it, and the direction of acceleration changes. For example, if a vessel is on a path and needs to change course to avoid potential incoming fire, with your 50G acceleration all it needs to do is pitch up five degrees with maneuvering thrusters and start a main burn. One second later it will be moving at 42.7 m/s along the y-axis more than its previous vector, meaning that unless the energy weapon fired at their previous estimated position is a laser with a 100-meter-diameter still possessing enough energy to melt the ship in a fraction of a second, or if they correctly estimated the course change and tracked the laser along the vector, transferring energy for longer, the ship will survive or suffer extremely minor damage. Remember, in space combat with lasers you're generally light-seconds or light-minutes apart, meaning you must shoot at where you estimate your target will be in x amounts of seconds, rather than shoot at where they are.
Yes, but it still limits where you can go and is slower than accelerating in the direction you want to go, for example you can't burn in the opposite direction from where you are going. Your projected location will be a cone, not a sphere. Omnidirectional thrust could potentially be achieved by a reactionless drive that operates without the need for thrusters, one such things could be projecting an artificial gravity well in the direction you want to go, that always has the same distance to the projector.
Unless you have absolutely perfect fleet-wide communication run by auto-targeting AI, the organization of this is somewhat questionable. Likely, task groups of multiple ships would be assigned to take out task forces of opposing ships, and the estimation of enemy positions could potentially be more likely when shooting between them (both are likely to change course to that location, as opposed to bracketing a single ship regardless of other enemy ship's positions). While in a perfect Stellaris world a fleet would eliminate enemy ships one-by-one to reduce incoming fire, in the real world it would be worth simply damaging enemy vessels to reduce their combat effectiveness. Every shot hit damages a weapons port, shield generator, or vents atmosphere.
One would think that, but it's not actually true. I have run the numbers and even if damaged ships can only do damage relative to their health, numbers still win. I assumed they would operate that way, the task groups themselves will focus their fire though, that translates to the same result on a fleet wide scale. I also don't think battles would be fought over a distance of light minutes, unless you have really slow ships, slow to accelerate that is. I would say a significant fraction of a light second perhaps. And distance between ships on one side would be within real time communication range.
All in all, what you are saying is correct in the current Stellaris mechanics, as they don't take into account damage when determining damage output per vessel. However, instead of shooting down a concept for missing an aspect that would make more balanced, attritional combat viable, I'd say add in modifiers reducing damage output according to how many hull points are lost on the vessel. This would solve the problem of focused fire being the only way to decrease fleet strength, meaning that Stellaris could move to battles in which fleets are damaged, not eliminated. This would remove the problem of empires not being able to come back from decisive battles, and allow smaller fleets to engage in attrition battles with larger forces.
Try to do the calculations yourself, it's actually easier to do if you take battle damage into account than not doing so. It doesn't actually make a difference. Focused fire makes a difference if two forces of equal strength engage in battle, in that case it makes a difference. But when it comes to doomstacks, it doesn't change anything.
Assuming perfected targeting computers. Detection is not as trivial as some believe, otherwise scientists would not be debating theoretical existence of 10th planet, instead they'd have proof.
That possible 9th or 10th planet is extremely cold, it receives very little sunlight, which means it has to generate nearly all the heat it can radiate away itself, either through the decay of radioactive elements or tidal forces. As a consequence it radiates very little, so we might not have sensitive enough equipment to distinguish it from cosmic background radiation. Spaceships on the other hand generate lots of heat, they would be impossible to miss. A single adult human radiates 100 Watt of IR light, and we can detect IR sources radiating 20 Watt at the orbit of Pluto. You might be able to delay detection for a few hours by funneling all that heat into heatsinks, but that has limits, and once that is reached, you'll light up like a signal fire.