It's not the
inconsistency that disqualifies it from academic citation, it's that it's a
tertiary source. The Encyclopedia Brittanica isn't a moving target if you cite the edition, but it's also a tertiary source, so it's just as citable as Wikipedia is, that is to say, not (except if you're treating Wikipedia as a primary source, eg you're
studying Wikipedia)
It's stupid to ban students from using Wikipedia- sure, Wikipedia isn't of uniformly high quality, but it can be a pretty good encyclopedia. It's just not something you're allowed to cite.
If a school doesn't want students to read Wikipedia at all they really should provide an alternative encyclopedia that the school thinks is high enough quality for students to use (but still not cite), I think you can get subscriptions to Encyclopedia Brittanica now? But that costs actual money.