I never understood the issue with the EMH's personality. It's there to be used in an emergency, do you really care if he introduces himself and says please or would rather he got straight on with the job and fixed the hole in your face thanks to Starfleet's engineers not investing in some fuse breakers?!
if he was only used as a short term suppliment then I don't see an issue. But in Voyager's case when he's the only doctor and there all the time, then you'd want someone with a better bedside manner