Sure, but that does not apply to the case we're discussing - which is a government paying clinics for procedures. You could substitute "a billionaire philanthropist" for "a government" and the outcome would be exactly the same.
Now if you want to talk free markets in general, then I want to point out that in the real world, a free market cannot thrive without some sort of government that ensures social stability and enforces contracts. Without such government, the market would quickly degenerate into trading violence alongside currency, and either disintegrate or... end up producing a government. Ultimately, "private enterprise" and "public governance" don't have a clear boundary between them - they're two modes of the same phenomenon, people negotiating with each other.
There is no billionaire who can even remotely approach the purchasing power of a government. If billionaires could truly influence markets, we'd have seen it on the stock market. Instead, we saw the Fed.
I am not proposing to get rid of the government, that leads to anarchy. A government is required to uphold the rule of law and, for markets, to sustain contracts. I would also argue that they should tax externalities. The trouble starts when governments go beyond that and start regulating and influencing the markets, ending up corrupting them.
Now if you want to talk free markets in general, then I want to point out that in the real world, a free market cannot thrive without some sort of government that ensures social stability and enforces contracts. Without such government, the market would quickly degenerate into trading violence alongside currency, and either disintegrate or... end up producing a government. Ultimately, "private enterprise" and "public governance" don't have a clear boundary between them - they're two modes of the same phenomenon, people negotiating with each other.