I mean how much does an academic medical center pay their Doctors? At UCLA the head transplant guy makes $2 million or so. Why not pay engineers more? You could probably justify it by taking a product oriented approach, with external sales or patents or whatnot.
Remember though: doctors are the ones who bring the dollars into medical centers. It is very easy to draw a line from an individual "rockstar" surgeon to the revenue they bring in. It is also the core mission of a healthcare organization to treat people, so doctors and nurses are the primary focus. There are enormous opportunities for software to make a difference, but this is hard to quantify except in very extreme circumstances (e.g. identifying systematic billing errors).
Right but you could make software a core focus by selling your product to other medical centers or doctors or whatnot. It would be hard to get it started but it should be possible.
I believe medical doctors are paid much the same as other scientists for research, i.e. the more time they dedicate to research the more money they forego.