As always, the best off'll still have more access to care, til they outlaw getting better care period. "Sorry you can't be treated because we didn't treat someone else, gotta be fair."
In the end, only reducing the cost of healthcare will make it more available to the poor. That will come from transparency & less interference from government (competition).
Most of the cost factor comes from medical schools limiting entrants. They mostly base admission on doctors' pay levels to keep medical care scarce and costly