The entire concept of the EMH in Voyager was wrong to begin with. He was run by the ship's computer, and instantly had an attitude and emotions and a desire to enhance his programming. Eventually he even fell in love.
First of all: why the hell would Starfleet allow such a program to run on ships? A medical emergency program would be very limited to the actual purpose, and nothing else. The idea that he has a terrible bedside manner alone is incredibly stupid.
Second: why the fuck is he more sophisticated than Data? The doctor understood the concept of humor, had emotions, felt love, never had any trouble with fucking contractions. Data would feel pretty damn old by now.
I mostly agree with your points, except the "terrible bedside manner," because first it was done from an outside-the-show perspective because he was funny, and second because it was based off of Zimmerman.
There was a way around the EMH plausibility thing-have B'elanna or someone on the ship greatly enhance or reprogram him early in the show out of necessity because of the long voyage. Otherwise, believing that what is basically a supplemental computer program could become as advanced as he did just by being "on" for a long time is just stupid.
If you play your Xbox games for long periods the characters don't become more developed and self-aware.