I would argue that for-profit hospitals should be allowed to operate because the profit motive is more likely to improve care than to make it worse. This will be the case so long as there are other hospitals nearby to provide competition for the for-profit hospitals.
If a hospital is in competition with other hospitals, it will have to provide good services if it is going to want to make money. This is a much stronger imperative for a for-profit hospital than it is for a nonprofit. A nonprofit does not get any tangible benefits from improving its services and, thereby, attracting more customers.
So long as there is competition, the profit motive should cause for-profit hospitals to provide the best possible care and the existence of such hospitals should not compromise care.