I don't think this is a post-MBA consutlant issue. I have a lot of ex-colleagues who were career consultants (meaning they joined consulting right out of undergrad) who left before being promoted to project leader / manger, if not even earlier before they get promoted from associate to consultant.
In general the turn over in consulting is very high. And the typical tenure of a role e.g. associate or consultant is 2 years. Some people move out not becuase they cannot make it to manager, but becaue they received an attractive offer outside and they want to move on to explore the world outside consulting or have more personal/family life. When you are a 2nd year consultant, sometimes the offer you get could be as good as a fresh project leader.