What I would like to see are minor injuries like they talk about in the revised system that they have on Tribble, however, if your crew gets injured more severely (perhaps a broken bone, dislocated joints, strange alien infection etc) the crew member could be beamed back up to your ship's SICKBAY for some period of time depending on the severity of their injuries or condition (perhaps an hour or two) before they could be used again.
In the meantime, if you're on the ground, you could substitute another of your MULTITUDE of bridge officers to beam down and continue the mission (or general Redshirts if you don't have another), and perhaps use another of your multitude of officers to replace their place on the bridge while they are recuperating in sickbay. I mean, your ship has these facilities onboard, why not make use of them?
Smaller injuries could be healed with "Medkits" or "Field Triage Kits" and whatnot, and they could be purchased on major bases or even found as dropped items from time to time, because your enemies would have to have these things too, you know? Larger injuries could be treated in SICKBAY with the suggested cooldown timer for the injuries to be healed.
In space, your ship gets pelted with all kinds of terrible weapons. Logically speaking, your ship should take damage over time, and take time to be repaired. I like the idea of minor damage to be done to systems, like the plasma conduits on deck five just blew out, and now your weapons systems have a 10 point deduction in power while your crew gets to fixing it or bypassing. Obviously, you could compensate by REROUTING POWER to the damaged system for a time, but it would still hamper you in some way.
Those kinds of things could be fixed over time, and perhaps have their time reduced by making use of your ENGINEERING TEAM ability. It already fixes your ship, so why not have it lower the cooldown on these debuffs to your ship?
But sometimes more serious things can go wrong. This is where you'd have to have items in your cargo bays and whatnot to actually replace damaged systems. These could be purchased from major bases like usual, OR for an equal amount of energy credits (plus an additional "Convenience Fee"), they could be replicated by your ship's REPLICATOR if you're out in Sector Space. Because let's face it, they can replicate virtually anything they need with them, and it would make the penalty much less invasive to gameplay, and make it more like a management of resources and upkeeping your ship, which really makes lots of sense in-universe.
This way, you can still deal with a "Death Penalty"and not make it the end of the world, even on higher difficulties, as arguably the increased credit payout and items would be able to compensate for the larger need of replacement parts.
THE SYSTEMS TOGETHER
Since both systems are making use of items and cooldowns, let's do this. When you're in Sector Space, the cooldowns for BOTH injuries and busted components will drop more quickly (say maybe 20-30% faster) than if you're in a mission.
This kind of "penalty" is completely "in universe," is logical, and will not make the system a major hassle for anyone, I wouldn't think. Injury items would be cost effective and not prohibitively expensive for lower tiers of players, and the same goes for the space items. And, you're actually USING YOUR SHIP FOR MORE THAN JUST A WEAPON. Your sickbay is treating your wounded over time, and your replicator is providing you with replacement parts for a cost in energy. In the future, perhaps you can replicate replacement inventory for your sickbay to make sure you can keep your officers in top medical fitness, and perhaps even have this set as an automatic drain to your credits, which can be turned off if one so chose at the risk of their sickbay running out of supplies.