I've had this conversation with a friend of mine the other day and he raised an interesting point.
When the NHS was first being proposed the doctors at the time were strongly against it. The Health Secretary (Bevan I think) just flat refused to listen to what the doctors were telling him. He told them that it didn't matter what their complaints were, he was going to start a national health service.
If we had a system where you had to be an expert in a field before you could be in government then we would lose things like this. We would also lose problems with idiots running things (cough Gove cough). Overall though, we would never have change, our elected officials would only ever vote to maintain the status quo.
Additionally, we vote for people to represent us in government, I don't know that doctors could ever truly represent my views on health care.
I would just like to add a note that none of the things that I've represented as facts above have been checked. I learnt them in the pub, they might be wrong. Let me know (nicely).