Sane healthcare would be one that addresses both sides of the equation... greed from unregulated for-profit healthcare that drives prices to insane levels due to supply and demand being broken (demand is infinite since people will give everything to live longer). It also needs to address the other side of the coin with highly-regulated universal health care, which is the lack of a free market to drive quality so things like wait times, availible medications, and other issues arise.
There are a few solutions to this but the best one I have heard is co-op based health care. Essentially healthcare where the owners are the patients of the companies they use, and there are no owners otherwise (so all owners are equal owners). When you move to a new healthcare company then you loose ownership in the old one and gain ownership in the new one.
This gives you supply-demand pressures that ensure your healthcare caters to what you want and need (or else loose their funding by patients moving), but keeps prices in check by eliminating the greed factor since any profits go back to the patients and insurance holders themselves.
I do agree that we can better address our supply of doctors. Though my views there are a bit all over the place. For starters if i really had my way completely I would totally take away any authority doctors have. I would make all prescription drugs availible over hte counter. This works quite well in many countries and doctors are now someone you choose to consult rather than whoa re forced to. This would eliminate the need for the AMA.
That said, i dont think id ever convince america to actually trust people to have autonomy over their own bodies, so I doubt that would happen.
The other thing id do regardless of anything else is make all job training, mentorship, tradeschools, and education free to all people at any level (up to and including PhD or medical doctor). That should address the supply issue to some extent.