I don’t have real data… but much of the medical staff in the US has a pretty strong union. So if this were the case, it would be because the union chose not to make it an issue in exchange for something else. Thus it isn’t really free overtime.

There are surely jobs for which there is no union and unpaid overtime is standard. So they would technically work more unpaid overtime.

That said, unpaid overtime should be illegal. Or the hospitals insurance should refuse to cover mistakes made during unpaid overtime, which would give the hospital reason to not allow it.