Not saying that this is good idea, but I think we'd need to take things at least this far to break capital dominance on battlefield
It's a result of fairly simple math.
Is strategic mobility important? No. Not to individual ships. There's no reason to keep frigates in case you want to do something quickly, they can't dart ahead of the main fleet.
Is tactical mobility important? No. Only some objectives matter and even then, they most likely won't change the balance of power. It isn't important to capture something quickly. In addition to that, battlefield is limited. The only objective is to destroy the enemy and they can't run indefinitely, there are borders against which you can crush them. Finally, fighters are substitutes for enough for frigates and some destroyers.
Officers multiply the strength of a single ship, so you want the individually strongest ships for highest absolute power.
Mobility irrelevant + concentration of power desired = capitals.
There are some ways I can think of that would make mobility more relevant.
First would be the ability to split fleet in campaign. Fighting patrols with just frigates might be preferable to fighting a heavy fleet response. Incidentally, Alex shot down this idea.
Second would be making objectives more important. Battle-winningly important. You would need frigates, if only not to lose right from get to. A variation could be, where both sides can only deploy their vanguard at the start (vanguard being ships of a certain burn level or faster) with a single, giant objective to capture. Whichever side does, they get to deploy their bigger ships, while losing side has to wait. If small ships can't compete, make it so that they don't have to.
Last way is to make it so that getting far enough into the enemy's side allows you to attack their reserve ships to some end. For example, losing logistic ships could increase for much CR the enemy side lost. This creates a way for mobile, hit and run tactics to win against inflexible fleets, while promoting balanced fleets. What good is destroying enemy freighters with a horde of frigates, if their cruisers reach your freighters and now you both are dead in the water? I suggested this idea in the past as well, to be discarded, too.
Battling concentration of power is harder and would most likely be about making AI more coordinated. I don't know how viable that is.
I don't like solving this issue with skills, but some sort of a bandaid would be making tier 4 or 5 leadership skill that gives some advantage to all frigates and destroyers, while the other boosts officers. You could tie this and previous idea together, by making small ship-friendly skill be squadron creation, which would be about buffing and coordinating small groups of ships.