I don't have an issue with the ships original medical crew.....you could just say they had a doctor, chief nurse, a few medically trained staff who perished during Caretaker and an emergency medical hologram.....for alpha quadrant missions, probably enough)
But i agree that not training staff after caretaker was ridiculous
More ridiculous for me though was the way they didn't bend over backwards to protect the doctor. You would think they'd realise his importance and pull out all the stops to create backups, safety nets, anything to ensure he was extremely secure and locked in for the coming decades
But instead, they couldn't give a toss....they continued to treat him like a screwdriver with no particular value or importance to the crew....during swarm, B'llanna has more important things to do when it appears that the doctor may turn into a cabbage and be lost....WTF!!...you lose this guy and you're screwed big time! Kes is the only one that thinks..."hey, maybe we should save the only guy on the ship that knows how to perform complex surgery and tackle unknown diseases"
Throughout the whole series, the bridge crew continually dismiss him as an annoyance.Seven takes over from Kes in being the only one that might recognise his value. In latent image, Janeway still perceives him as a piece of irritating technology. Hell, even in Endgame, old man Paris talks to him like he's a jumped up lightbulb....."you've called yourself Joe and married a human female....really, but you're just a pointless thing"
If a violent crazy super alien made me choose between keeping Janeway or the doctor alive.....i would not hesitate...Chakotay or Tuvok could do an adequate job running the ship...heck, even Kim....but who could replace the doctor....no one!!