Of course, I can't prove that from scratch in a HN comment. What I can do is point out that in the science studying this, it is an uncontroversial fact.
I didn't substantiate that, which made it less convincing, but here is an Economics textbook saying the same thing: https://pressbooks.oer.hawaii.edu/principlesofmicroeconomics...
I know, you can think of an externality. Trust me, Economists can also think of externalities, far more than you or me. In general, they just add interesting nuance to the supply/demand model. They don't completely invalidate it.
But I can't easily demonstrate that, so I suspect I have not changed your mind.