"Rich doctor" is a thing only in the U.S., and that's due to collusion and price fixing, not because American doctors are better somehow.
In the rest of the world doctors are basically like white-collar car mechanics, and often earn less money and respect.
That's false. One example:
"According to the Government of Canada Job Bank, the median annual salary for a General Practitioner (GP) in Canada is $233,726 (CAD) as of January 23, 2024."
That's roughly $170,000 in the US. If you adjust for anything reasonable, such as GDP per capita or median income between the US & Canada, that $170k figure matches up very well with the median US general practitioner figure of around $180k-$250k (sources differ, all tend to fall within that range). The GPs in Canada may in fact be slightly better paid than in the US.
This is a reach. Can you share a few examples of Western countries where that is the case?
It's about the same pay as a (professional) engineer. In the US, both engineers and doctors are very highly paid. In the UK and Japan they are paid about 50-100k if experienced, which is somewhere about 2-4x less than their US counterparts.