It has never been a BL thing…. It’s all private schools and it’s been this way since most private schools starting accepting students. The entry ( first grade or now ore first) age has always been later then public schools so if you enter at one of the later grades the school asks you to “hold back” to be at age with the others.

Was it developed for the elitist ? Of course!!
Today they refer to these schools as “elite private schools”