Do a search for "Hospital Deportations", it's a real thing - a few other places have done it too, but Arizona lawmakers condone it - most other places told the hospitals to cut it out once they got wind.
And Single Payer is quite motivated to improve - that's like saying the Fed isn't motivated to work on better military projects since we're already at the time by a mile for military technology. If Single Payer isn't motivated to improve why did England for example go from one of the worst places to get a knee replacement surgery to literally the BEST IN THE WORLD? [And similar with Sweden being at the top of the pile for neurologic, although I'm not sure if they were always good or if they improved - might have always been awesome at it even pre-SP]
Motivated to figure out savings is a more rational argument but usually the Fed does try to save money as well, just once they do they funnel the savings into something else creating a net zero gain when it comes to finances, but a gain when it comes to service provided.