As the closest, and best, hospital near us is public, we go there. As we have PHI, I expect some level of "benefits". If all that means is that I get a private room (if noone else needs it), awesome. However, it means one of us gets a bed with the kids; or I get one with DH (or he with me); we get a choice of dr, nurse, midwife, specialist, etc; choice of meal; longer visiting hours; and a few other little things.
All great- being able to stay with DSS when he is kept in because his oxygen is low, is a huge deal to us. If we went public, this hospital would not allow that. But with PHI it does.
What it comes down to is money- if hospitals want to treat everyone equally (whether they have PHI or not), they shouldn't get money from PHI patients' cover. Can't have it both ways.
ETA: and if people really want public and private to be separate, we shouldn't need a medicare card to apply for PHI.