This idea is not all that new but I want to put a slight spin on it. To sum it up: Make Crew Matter.
Right now Crew are meaningless. They help you to recover hull HP when you have active crew but that lasts all of a few seconds in most combat. This is even more insulting for huge ships with thousands of crew. Their crew gets wiped out from the first couple torp hits or the first warp core breech that their lumbering ship cannot get away from but survives.
So first thing is first... Crew should become incapacitated (because they supposedly are not killed) via a numerical value NOT a percentile. The same Torp hit should not lose a Defiant 5 crewmen when it loses a Bortasqu' 500. That would be to say that the Bortsaqu' has a lot more crew but crammed into the same area that the Defiant had so as to arrive at immense population density which is absolutely absurd.
If we make this change alone the big ships would get more use out of having big crew numbers as each scratch would not utterly annihilate their ENTIRE crew. If the Devs feel working with numbers would be hard due to how few crew some ships have then perhaps you need to scale up the number of Crew. A Nimitz Class carrier here on earth supports around 5,000+ active crew including its flight teams. That is the same size roughly as a Constiution. Something like an Odyssey should be boasting several TIMES that much crew and the behemoths that are carriers could easily have crew in the Tens of Thousands.
Next I would recommend having your many crew help in other ways. Faster recovery from subsystem damage, faster power rerouting, faster non-tactical team enhanced shield distribution (when you hit the button, this would not interact with Tactical Team's ability in any way so as not to make it better than it currently is which would be crazy), and last but not least a TINY boost to cool down speeds per every 50 crewmen. This last boost should be very small but still just enough to make it ever so mildly worth caring about.