MBA after MBB for advanced degree professionals?

Hello,

What are your thoughts on pursuing an MBA after 2-3 years at MBB?

As a physician in my 30s turned consultant at MBB with no formal prior business education, I am contemplating whether it would be useful to pursue a top MBA (if I can get in) after a few years at MBB (let's say after I reach the manager level).

I have heard some mixed opinions, from "yes absolutely necessary, positions at/above that level are rare if you don't have a top MBA", to "not needed in your case, too old to rebrand yourself with an MBA, plus MBB already provides some legitimacy as far as brand recognition".

Ultimately, I would love to stay at MBB, but knowing how hard it is to go up, I will realistically have to pursue a different career down the line. Something in healthcare (VC or hedge fund if do-able?) Or if you have any other suggestions, I would love to hear what other healthcare-related fields you think I would be a good fit for.

Of note, finances would be an important consideration as well. Even if somehow MBB were to fund my MBA entirely, I have massive med school loans to pay off and taking 2 years of re-payment would not be totally insignificant. But I would 100% consider it if deemed an important step to further my career. 

Thank you.