I can only talk for McKinsey Europe -that is indeed different than many of other offices-. There are several specialization tracks, called L2 and L3 (e.g. Telco/Retail L2 practice)
BAs can start an specialization track (L2 specialization) at least after 2 years at the Firm, when you have also relevant experience in the field in terms of past engagement. However, as an Associate, you can apply before for L2 -given that you are more tenured and experience, but it also depends precisely on this prior experience before MBA or others-.
The reasons why are mainly (i) having well-rounded profiles who are all-roads and (ii) giving you the chance to try differnt things when you are still starting.
Hope it helps!