Did Tom have first aid training prior to Caretaker? I only remember him saying he had "half a semester of biochemistry" or something like that.
Anyway, Voyager didn't need more medical staff because Robert Picardo was part of the main cast and wasn't slated to be killed off. They would only have had to worry about it if the actor (heaven forbid) had died during the making of the series, and then maybe they'd have brought in Andy Dick full-time. And they did know they'd get home in 7 yrs, not 70, since TNG had gone 7 yrs and the staff probably didn't envision Voyager running any longer than that.