If it's anything like Europe, doctors and hospitals get to charge extra (not covered by the state medical insurance) if the patient is in a private room. Plus the private room itself costs extra too.

It has different names depending on the country.

PS. private medical insurance may cover the private room thing. Also, doctors are effectively incentivized to give private room patients preferential treatment. So it is one source of inequality in Europe's health services.

In the article there's a whole section about how hospitals are removing non-private, (aka "normal"), rooms, to replace them with more-profitable private rooms that patients pay for out-of-pocket, (and, since they're not insurance companies, can't negotiate better rates).

Many hospitals house patients in shared rooms with two (or more) beds separated by a sliding curtain. It's cheaper, and is otherwise basically all downside, as jbeales says.