At least in SotS2, it wasn't that individual ships developed quirks, it was the design itself worked better (or sometimes worse) than anticipated. However, being a 4X game, those quirks were a lot more powerful and drew from a fixed list. Less 1% faster and more and more +25% range with ballistic weapons or -10% turn speed and thrust speed.
I agree though that ships themselves probably shouldn't have those kinds of attributes. But I would think that a related thing would be possible, that of ship reputations.
If a ship either did well in a particular battle, survived overwhelming odds to escape, or even sacrificed itself to save a civilian fleet, that ship could gain a reputation and gain a small crew morale bonus because that crew is serving the THE HMS Victory which is a prestigious posting.
You could even go as far as something like from the Honor Harrington series where these ships have their honors passed down to the next ship such that there's always an HMS Nike in service, so even 300 years later, it's still THE battlecruiser everyone wants to serve on. But to do that, you have to decommission the first ship and transfer its name and honors to the next.
Now to make the code simple, maybe just let the player decide which ships have these reputations. I'd hate to try to figure out what counts as a heroic sacrifice or anything. Just limit the player the number of distinguished ships the player can have before some sort of penalty is applied. After all, if all ships are special, then none of them are.