If I was to base this vote on logic alone, the answer would be no. It seems obvious that the more you pay someone the worse they will preform. In science this a hypothesis. However, it is not true until tested and verified. Thankfully, the peer reviewed literature is extensive on the matter.
The results overwhelmingly demonstrate that incentives work well for mechanical/straightforward tasks. However, they do NOT work in situations requiring critical or creative thought. In fact, incentives appear to do the OPPOSITE, in effect hindering innovation because narrows focus when broad thinking is required. This effect continues to worsen in proportion to the amount used as an incentive! Pay people enough to be comfortable and allow them autonomy and they seem to thrive with such tasks that appear internally driven.
Moreover, the commercializaion of healthcare shifts the incentives toward treatment of symptoms and prescription of costly, often unnecessary and sometimes harmful medications instead of prevention or cure of disease. Privatized healthcare prioritizes profit over health and wellbeing by necessity..
Even in the presence of massive waste and inefficiency in the health care industry, the potential profits to be made attracts the top talent from around the world. Top talent, often pictured as the brilliant doctor from a poor country, also extends to health care corporations. Lower pay and less competition (in addition to more waste) will drive the most talented people in the US elsewhere, in addition to failing to attract others.
A single payer system does nothing to encourage ingenuity. If a person is going to be paid no matter how hard they work, or no matter what they invent, they will not work as hard. By the same token, a single payer system has no competition, so they have no reason to work harder or to develop new products.