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.
I think your ideas are not only good for the game but they also make common sense.
Adding to your idea, I think that certain crew numbers should reduce the cooldown for Sci Team, Eng Team and Tac Team abilities. (These cooldowns should NEVER affect the minimum global cooldown, however.)
At the very absolutely smallest minimum, torps and mines shouldn't be disabling/killing 10-20% of a ship's crew, especially when it is fired from the world's weakest, puniest, level 1 NPC Miranda or Bird of Prey against the biggest, baddest, toughest level 50 cruiser or carrier with every bit of hull and shield resist that can be mustered.
It's a bit ridiculous. Be in PvE or PvP. At the absolute least, they need to change the 10% and 20% to just 1% and 2% for kill or disable. That alone would go a long way to making it a lot less ridiculous in just how much crew can be lost.
On top of that, Theta radiation should have it's amount of crew death be lowered significantly. It's rather ridiculous how fast it can wipe out an entire crew.
Then actual crew recovery, should be possibly sped up, possibly. With the major reduction of crew loss, then it might not be so bad even if you do gain back crew slowly. If it was considered an issue still, then maybe buff up Biofunction Monitors.
And the Nurse DOFF is nice, but it's only a bandaid fix, and it takes up a more useful DOFF slot.
Once all that is done, then I feel that crew can be altered in other ways to be worthwhile.
I fully agree with the OP's idea. With the exception of raising crew quantities.
Infinite possibilities have implications that could not be completely understood if you turned this entire universe into a giant supercomputer.
Supporting this! Make the 'crew damage' numerical damage not percentage damage. It's stupid that a cruiser looses crew at the same rate as an escort.
Also, i think i heard this on some podcast from Geko, the initial implementation of crew was intended to be more complex then it is now, allowing you to allocate crew to subsystems of some sort, probably in the way you allocate the power levels now, but this seems got ditched along the way... lazy bones.