Medicare is just as expensive, and the government is what makes drugs, doctors, malpractice and opening facilities so expensive. So no.

Other governments don't have a problem making it cheaper.

You will also find other governments with public healthcare make a complete mess of itself.

What makes health care expensive in the US is not public vs private, its the regulatory framework on everything. On drugs, on hospitals, on insurance, on doctors, on malpractice, etc.