I don't think attrition would solve the issue here at all, in fact i agree with some of the posts above that it would just create more issues. Imo the problem with fleets and the space combat in general is due to a number of issues.
1. Ship and fleet "stances" are practically non-existent. All we have is generic offensive, defensive or "balanced". Really though these do little to change the outcome of a battle, numbers and fleet power is all that matter imo.
Ship stances should dictate what kind of role that ship takes in battle beyond the simple, does it rush forward or hang back. For example, anti fighter/missile stance for corvettes, escort/screening stances for destroyers etc.
Fleet stances would dictate the overall behavior of the fleet, so does the fleet break formation and rush to the attack, dependent also on individual ship stances, so your ships with a some sort of attack stance would rush forward. Or would it maintain formation and move in as a unit, with attack stance ships rushing forward only when the rest of your fleet is within range. Or would it hold position and wait for the enemy fleet to move in. Etc.
2. Ship formations. Currently we just have this rather boring diamond formation with i think the largest ships at the front and the smallest ships at the back. That to me makes no sense. Imo having your largest ships in the back or in the core of your fleet, thus flanked by your smallest ships, would make a lot more sense. Those large ships are expensive after all and you'd want to protect them. So some options for fleet formation would be useful and provide some additional tactical options to the player. These fleet formations would of course link in with the ship and fleet stances.
3. Ship types. I think the ship types could be expended some what beyond the current 4 that we have. For example, where are the dedicated carrier class ships at? What about dreadnoughts? Frigates? etc. A wider variety of ship types with their own pluses and minuses opens up more options for fleet composition.
4. Fleet caps. Now i realize this isn't a popular idea with everyone but just hear me out. I think that a soft cap on max fleet size would be something that could add more realism and choice to the game from a strategic or tactical point of view.
Something I suggested on another thread was to have a soft cap on max fleet size, this could be linked to your max logistics and or a separate tech and modifier, perhaps even with a boost to it from an Admiral. Going over the soft cap would be possible but it would come with a down side. This would be negative modifiers to speed, evasion, FTL speed etc. This would give the player a choice in so far as, do you go for overwhelming firepower or improved combat ability, do you want a fleet that will go in and destroy everything or do you want a fleet that can perform quick, surgical strikes against enemy positions before retreating etc
This could be combined with a supply limit per system, which would prevent you from clumping multiple fleets together in one system. The supply limit in enemy systems would be higher the closer you are to your own systems. You could increase supply limit by having dedicated supply ships, or a supply station that could be built in enemy systems. This supply limit could again be a soft cap which when gone over negatively effects the ability of your fleets.
5. A wider variety of weaponry and defensive components with more distinct advantages and disadvantages between them. Right now we have a Rock, Paper, Scissors system which, whilst it works, is boring as hell imo and generally leads to the same tried and tested load outs in each game.
6. Link all of this into each of the different nation archetypes and perhaps ethics and traits. For example Honourbound Warriors or whatever their called would be more likely to go for fleets all about the firepower with direct engagements between large fleets being their preferred style. Peaceful nations might be more inclined to go for smaller defensive fleets, perhaps with speed in mind over firepower. Hive Mind nations might go for large fleets of small ships designed to overwhelm their enemies with numbers etc.
I think all of these changes would improve combat in the game immeasurably whilst also forcing the player to change their tactics and strategy based upon who their fighting. In other words doomstacks would have their uses but they wouldn't be the answer to every problem.