Not quite the case. It is a fair generalization but I know doctors and lawyers with accents. If your abilities are only average for the profession you are entering then it would very much be an advantage to speak grammatical Standard English. Those accents that do not dispense with proper grammar and construction do much better in the professions than those that have a debased structure. Ideally one's sound should not take a listener's attention from one's message and that works everywhere for Standard English and it works for the grammatically correct regional accent of the doctor setting up shop in the region whence he arose.
Having an accent is not the same as being unable to speak proper english! Yes lots of doctors have Indian accents, but they speak ENGLISH, and some of them better than most americans.
What the poor blacks often speak is not anything remotely resembling proper english. Bad Grammar is not an accent.
Agreed. There are quite capable communicators of the English language who nevertheless have distinct accents, or even take a regional license or two.