It probably would work if you had a large enough pool of people, but how much bigger can you get than if 300 million people were pooled together and collectively they negotiated rates on drugs and doctor visits? Thus the ultimate idea of some form of universal coverage.
Where your idea kind of falls apart is that you need someone to manage all this. Good luck getting Kenny in apartment 5D to take care of this when he can't even turn the volume of his TV down after 10 PM. But I think obama care kind of does this on a state level. I could be wrong, but I think that's what the various marketplaces they talk about are. But each state manages it differently. Not shockingly, red states tend to mismanage things and offer worse services than blue states. In the end it is all a crutch. This should be on a national level like every other industrialized nation offers.