Maybe I'm not thinking this through right/maybe it was covered in an episode (that i missed). But I always wondered why the crew couldn't program an medical team rather than just one hologram and enroll Kes & Mr.Paris. Couldn't they request another? Perhaps with less skills+experience but one that could easily handle itself just as well if not better than the pilot of the ship. Maybe a holographic nurse could've been whipped up especially in emergencies.
Ps i seem to recall the episode Latent Image when the doctor faced a massive ethical dilemma over which crewman to save...surely a med-bay with more holographic assistants would've resolved the docs issue.
Or wait for it a stasis chamber which we know the ship has, and with only having one Doctor onboard and no nursing staff to speak about would make sense to have at least one availble at all times so you can freeze someone whilst working on another.
Sorry I think I was applying some logic, please forgive me.
Yes, Latent Image is an interesting episode don't get me wrong. But when you think about it - they could've (As you say) put one of the injured in stasis or have one or two holo-medical programes to assist in such scenarios.