Personally something I wanna point out with the OP idea I can see is that it promotes snowballing. Starsector combat is already kind of sink or swim, and while it may feel satisfying to rapidly get a half dozen kills with your flagship and provide your fleet with a whole 15% boost in damage, or something, it's a 15% damage boost deployed against a fleet that you probably now outnumber and outgun already. Basically, by the time that you get the buff to a significant level, it's too late to really matter.
I suppose the perk idea does make possible a "mega-murder" strategy where you deploy your fleet against an enemy that far outmatches yours, but you equip a flagship with high-power burst killing weapons (such as missiles) and just blast all the ships you can before either fleet can fully commit. But that sounds less like a "strategy" to me so much as flexing on the AI because you leveled the "one man army" tree. And as much as people complain that the current combat tree is a shadow of the old one, full treeing combat basically turns you invulnerable in .8 and you can pull the maneuver I described off anyway. Combat+Tech is basically the most lethal" way to level yourself, focusing on all the "piloted ship" buffs with only 3 points spared for getting yourself +10% OP because, uh, come on.
Of course, what someone with skill "can" do and what the general player base is aware of or is also capable of pulling off is not one in the same. The real value of the idea as outlined in OP isn't actually the mechanical effect, it's the "feeling" of it. Logically, 20% damage boosts when you outnumber the enemy fleet 2 to 1 doesn't matter at all. Emotionally, it's a great way to encourage players to try a combat-focused playstyle when they may otherwise think it's not useful. In reality the combat tree is PLENTY useful, it's just harder to see (how is +150 armor for the purpose of DR going to help me kill things?). The suggestion in this thread OP would be "visible" enough to seem like a good idea.