And it is happening in New Zealand.
There used to be a funding/provider split in the public health system so that if (for example) a private hospital could do certain operations quicker, cheaper and to the same standard (or higher) than a public hospital, they would gain the contract. The focus was on the best outcome for patients, not whom owned the buildings (often same staff in fact).
Annette King changed this and in 2002 very good hospitals like Wakefield had their contract for cardiac surgery cancelled. Now of course the public hospitals can’t cope and they have asked Wakefield to help out, but of course Wakefield downsized its staff after losing the contract. So the bottom line is patients do not get operations and die, because of ideology.
We see the same mind-set in Corrections, where a hugely sucessful privately managed (not owned) prison has had a law passed just to stop it renewing its contract.