> But in your example Medicare is just a really big insurance company
I agree that there are better examples of government regulation directly impacting medical practice, but this example illustrates the power of a monopsony[0].
To overgeneralize, the same way that monopolists (single suppliers) can exercise power over purchasers in ways that we might deem unfair, monopsonists (single consumers) can exercise power over suppliers in ways that we may also deem unfair or harmful.
These effects are not limited to Medicare patients or providers, by the way. It's not hard to make the case that customers who can choose between Comcast and Verizon FiOS are harmed by the fact that cable companies are regional monopolies in most other markets.
Similarly, even if you have a private insurance plan, there are a number of ways that you are affected by Medicare's policies indirectly, in ways that you would not if they weren't such a big player.
[0] https://en.wikipedia.org/wiki/Monopsony