But to be able to play at the top of the field you'll have to have attended something like Penn Law or Yale Medicine. SUNY Downstate won't cut it.

It's somewhat backwards in medicine. Many top grads stay in academics where the prestige is high but the pay is low. With the exception of elective plastics and dermatology, the highest earning physicians tend to be from middle of the road schools and work in rural areas after graduation (commonly from surgical sub-specialties).

It will, it’s just substantially harder. The ranks of partners at top law firms are much less prestigious than those of top law faculty. Academia cares more about prestige than basically any other sector of the economy. Even in medicine you have many, many tries at associating yourself with a high prestige institution throughout your career. If you studied at a toilet tier Caribbean medical school but ten years later you’re working at the Mayo Clinic no one will care about where you got your degree.