Is a Stellaris Battleship just a later model Corvette?

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And no duh, this is space not an ocean, but last time I checked, the Dev team for Stellaris is the group that set the naming conventions using those for RW naval warships of the 20th century, not me. Science fiction writers have been using those tropes for almost the entire last century plus, with some going so far as to create SFUs that try to replicate sailing warship conventions. And there are practical considerations of the vessels used in space flight (and fight) that would see them mirroring naval conventions.
Most of the SciFi authors tend to obey relativity theory as well as other general laws of, by us perceived, nature, thus bigger size is being translated in more mass and more power because more weapons and other military equipment. If the design followed alternative theories about space and time, we could even have ships made of pure energy, deadly battleships of the size of a corvette, or ingame redesigning of the galaxy map. Though it would be more difficult for our human brain to visualise it because the images would be thoroughly virtual.
 
Most of the SciFi authors tend to obey relativity theory as well as other general laws of, by us perceived, nature, thus bigger size is being translated in more mass and more power because more weapons and other military equipment. If the design followed alternative theories about space and time, we could even have ships made of pure energy, deadly battleships of the size of a corvette, or ingame redesigning of the galaxy map. Though it would be more difficult for our human brain to visualise it because the images would be thoroughly virtual.
Where does relativity theory cross over to "bigger is better"? Are your battleships massive enough to cause lesser ships to be caught in the larger ship's curvature of space and start orbiting? Then you start talking about something that sounds like Tier-11 technologies as though they're at all pertinent to the discussion.

Oh, and "most" science-fiction authors historically haven't really kept in mind special or general relativity, or many other laws and theories in physics or chemistry or other sciences. Those pesky bits of science often get in the way of a fun and interesting story. A significant fraction of sci-fi authors DO keep at least some of those things in mind, but are just as likely to specifically break one or more of those rules as well, again in favor of a story element.

If you're interested in viewing these things through the lens of science, take a good look at the Square-Cube Law and then tell me whether bigger is necessarily always better.
 
If you're interested in viewing these things through the lens of science, take a good look at the Square-Cube Law and then tell me whether bigger is necessarily always better.

L-Cluster Resident: "Therefore, being nanites is best. We told you so."
 
Unfortunately we're sort of stuck with a hybrid situation. The ship system seems to be designed from an end-game-tech point of view with ships intended to have differing roles similar to 20th century navies. The tech system however doesn't really go along with that idea. As OP says, historically all ship classes got bigger over time; we didn't invent patrol boats, then destroyers, then cruisers, then battleships. If anything it was the other way around: build the biggest ships you can support first and when they get too big to use for some tasks you invent smaller classes for those tasks.

EDIT: If you wanted a more historically-oriented tech tree you could probably introduce all the ship types from the start but with new sections becoming available over time with more and more weapon and aux slots.
I love your description of the development path. I also agree with the idea of having all four initial classes at the beginning, as I'm never entirely married to any of the dozens of ideas I've thrown out there over the years. I put together an idea for starting all of the classes with a default same-size-slot loadout (e.g., Corvette all S-slots, Destroyer all M-slots) and then unlock techs that allow for consolidating slots to make bigger ones, switching slots from utility to weapons or vice versa, and finally adding new slots on either or both sides. I could easily see that integrated into this other idea, starting the game with the smallest configurations and working up to larger ones, both by slot size and quantity of slots.

With that, you could keep the same four classes, while allowing each to get bigger, stronger, and tougher through the decades. You'd have to pay more for ships built with the newer hull sections, but they would allow for higher speeds, max Evasion, Hull Points, etc. A more advanced stellar navy would have cruisers that are easily a match for another empire's battleships. As with anything else, you'd have to make a ton of parallel changes to make it work, but that could open up a number of other improvements and fixes at the same time.
 
I started looking at that hybrid slot expansion and size increase, and thought that you could have the following configuration pretty easily:
  • Tier-0 - each class has three sections each with one weapon and one utility slot, with the slot size being effectively S-slots for Corvettes, M-slots for Destroyers, etc.
  • Tier-1 - each class adds a second slot each for weapons and utilities per section, but no consolidating yet.
    • This incorporates a doubling of the hull section's volume and mass, along with hull points, costs, build times, etc. (i.e., a Corvette with Tier-1 hull sections is roughly equivalent to a Tier-0 Destroyer)
  • Tier-2 - each class can consolidate two slots of the same type and size to create a single larger slot (e.g.. a Corvette can use an M-slot or equivalent weapon, like a Torpedo; a Destroyer can use an L-slot or equivalent weapon, like a Hangar).
  • Tier-3 - each class adds a third slot of their original size for both weapons and utilities per section (e.g., a Cruiser would be able to have an X-slot weapon and an L-slot weapon in a section).
    • Note that X-slot is just a placeholder size, and not specifically the vanilla Big Ass (tm) forward-fire cannon - you can also have X-slot utilities. Or it may be easier to change the nomenclature to a more straightforward A-slot, B-slot, etc.
    • Again, this is another size increase, this time to x3 of the original values (i.e., a Corvette with Tier-3 hull sections is approximately between a Tier-0 Destroyer and a similar Cruiser).
  • Tier-4 - each class adds a fourth slot of the original size for both weapons and utilities per section, and these last two can be consolidated into a single larger slot (e.g., a Destroyer can have either two L-slot weapons, one L-slot and two M-slots, or even four M-slots in a section).
    • And a last size increase, this time to x4 the original values (i.e., a Corvette with Tier-4 hull sections is effectively the same size as a Tier-0 Cruiser).
  • Tier-5 - each class can consolidate their two larger slots in a section into a single jumbo slot (e.g., a Battleship would normally have four X-slots per section, but could consolidate once to get two (double-X) D-slots or a second time to get one (triple-X) T-slot).
There would of course need to be very large changes needed to make this possible and then a bunch more to make it balanced. But it offers a relatively clean way to keep the basic classes while allowing them to expand in capability over the decades/centuries, not just in the quality of any given component or system.
 
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I brought this up in another thread quite a while back, but a way to look at the progression of weapons from S-slot to (triple-X) T-slot is to compare it to some of the more common deck gun sizes. If you start an S-slot as a 5-inch gun (found on many modern frigates and destroyers), and then increase them by the cube-root of 2 (x1.26), you get something like this (with an early 20th century (close) equivalent):
  • S-slot = 5.00 inches / 127 mm = 5"/51 caliber gun
  • M-slot = 6.30 inches / 160 mm = Canon de 164 mm Modèle 1893
  • L-slot = 7.94 inches / 201.6 mm = BL 8 inch Mk VIII naval gun
  • X-slot = 10.00 inches / 254 mm = EOC 10 inch /45 naval gun
  • D-slot = 12.60 inches / 320 mm = Cannone Navale da 320
  • T-slot = 15.87 inches / 403.2 mm = BL 16 inch Mk I naval gun
Please note a couple of things: as in the previous comment, X-slots and larger have nothing to do with the vanilla spinal cannon, and are just larger turreted weapons; and the table doesn't even get to the 18.10-inch 46 cm/45 Type 94 naval gun mounted on the Yamato-class Imperial Japanese battleships (they were initially designated as a 40 cm (15.7") gun to try to hide their actual treaty-breaking size).

Also, if you're looking for a spinal cannon concept that might work with the previous comment, take a look at this comment from my early attempt at a similar system.