I know things have been rebooted and revamped, but in my era (and, therefore, in my head canon) Bruce and Babs were a lot closer in age (Babs was about 25, Bruce 30 and Dick only a teenager), Bruce had no mentorship role and, in fact, Barbara had originally been created for the TV show as
a potential love interest for Bruce.
So, the thing in "TKJ" cartoon, didn't bother me for THAT reason (in fact, Moore's original story was, of course, an outgrowth of the silver age continuity), just for every thing else.