There are a few misconceptions in your question.
The first is that the vast majority of doctors in the USA are not US government employees. The US government does employ several doctors, be it through the military, Veterans affairs, certain public health programs, the CDC, etc, but the majority of doctors in the USA are employed by private healthcare providers. Also, the government tends to pay less than the private sector.
That and plenty of employers will certainly pay $50 an hour or more. Most doctors aren't paid by the hour, either, as it happens. Most bill for the services they provide.
And why do doctors earn so much? A few reasons- one is that it is very skilled, demanding work and requires very highly-trained professionals to do it. It takes 8 years of college to even start working as a doctor, and several more years of residency (which is not that well-paid, either) before you are a qualified specialist. Only then do you earn the big dollars, and it takes a while, and you work for it, day in, day out.