She could've gotten bored waiting and bumped off an unwitting redshirtNo assumption whatsoever.
Can you imagine Kes running into sick bay every morning for months always with the same question... "Has someone died yet who I can pull to pieces for fun?"(Kes returns the PADDs.)
KES: I've finished these and I'm ready for more.
EMH: You've finished those already?
KES: I enjoyed studying anatomy. It would be interesting to see an autopsy sometime.
EMH: What are the bones of the middle ear?
KES: Malleus, incus and stapes.
EMH: And the connective tissue between the middle and the external auditory canal?
KES: The tympanic membrane.
EMH: Hmm. I suspect you have an eidetic memory. An astonishing gift. I'll do a full neural scan on you at some point.

Also for a species that lives only nine years and develops to adulthood within their first, they would have to be able to absorb and store a considerable amount of information quickly and easily, so in that regard she is the best candidate to train as a medic.
What about the ship's life science specialist (the biochemists and xenobiologists onboard) wouldn't they have made decent medics, already knowing some of the basics. Then there are going to be those who underwent the same emergency medical course Worf did, making them basic field medics. Then there is the Juliet Jurot conundrum.