I have a suggestion, though it may be difficult to implement.  When I play, I generally focus on capital ship leveling, leaving the smaller vessels as (generally) cannon fodder, until I have several Level-8+ ships, which I group maybe 6 to a fleet.  I rarely have a fleet without a capital ship.  In any event, I've always thought the moniker "Flagship" added to whichever is the highest-level starship you have was rather neat.

My idea has a few parts:

1:  We have to recruit additional capital ship crews, so shouldn't we also get to pick the captain from a selection of however many crews there are?  For instance, the free capital ship would have a basic commanding officer with no buffs, but once you researched the next capital ship, you'd get a commanding officer with various buffs/debuffs that you could assign between your ships.  You may have one commanding officer that increases speed/decreases jump time, but lowers overall combat ability by a small percentage (call him an explorer), another that increases shields over weapons (maybe call him cautious), another that increases weapons over shields, but maybe one that allows a ship to survey a planet from orbit, to look for artifacts (scientist), allows it to capture resource drills (marine), or allows it to increase growth rate on a bombarded planet (doctor).  This would both add abilities to capital ships that opponents may not expect, and increase the variety of gameplay options.

Everyone expects a Kol to be able to take out pretty much anything, but few would also expect it to mitigate the damage done by their bombing runs.  In a similar fashion, people wouldn't expect to find an Akkan or other colony ship with buffed weapons.

2:  Every capital ship should have some influence over the fleet if its in, if it's the senior vessel.  Correspond some light fleet buff to the level of the senior capital ship, and its captain's powers (making him a commodore at level 5 and admiral at level 8 [or something...]).  I see why the Akkan specifically has a targeting computer upgrade, but the leadership found on a large ship would probably assist ships even without that.  It wouldn't have to be anything huge, but the roleplaying value plus the value of differing gameplay would be nice.

For instance, the weapon guy would increase refire or damage by a few percent per level, while the shield guy would do the same to shields, etc., while the specialists would require more creativity.  Buffs wouldn't stack; three level 10 ships cannot -all- be the flagship of a fleet.  This would encourage people not to group all of their most-experienced ships in the same fleet, as the boni would be better-used in other fleets.  It'd also, perhaps, encourage people to have multiple, specialised fleets rather than just unleashing their entire armada all at once on the same dead asteroid.

This may be grossly-diffcult to integrate and I doubt that my actual idea would make it in full, but the diplomacy expansion seems like a cool place to integrate more story and characterization to the game, in the form of actual people under our command, and making it so that every level-10 Kol isn't the same in every game.

This could even be tied into the diplomacy system somehow; I don't know.