But rich people are not charged because they are rich. They are charged because they have insurance. And it is insurance that has led to this bizarre situation

But rich people are not charged because they are rich. They are charged because they have insurance. And it is insurance that has led to this bizarre situation where the free market is completely broken and you can't confidently put a price number to a medical product or service. If almost everyone was paying for their medical care out of their own pocket we would not be in this situation. And there are plenty of other countries where this is the case. In India for example, individual doctors literally have a board with a list of what they charge for various services, and if you visit a hospital, someone at the reception would be happy to help you with these. You want a general ward? Here's the price. You want a private air-conditioned room with five-star catered meals, here is the price.