Well yeah for Heart Attacks, Stroke and the like it wouldnt mean as much.
For shit like Hernias, Cancer, Knee replacement Surgery, etc. that is important but not a get treatment In like an hour tops or you are gonna drop dead/suffer severe brain/heart damage it will certainly help. People can and sometimes will pick and choose based on price or perceived quality.
that's the issue; there's very little evidence that consumers know anything about health care and lots of evidence that they really don't know anything about health care. hospitals would start paying a premium for good bedside manners and compliance with patient requests rather than medical knowledge or skill.
anyway this would all be predicated on hospitals refusing care to poor, dying people so that's one thing that you'd see more of
consumers know pretty much nothing about anything they buy, other than cost, and people telling them that its good or bad.