I suspect drama schools have the hold they have today over the profession for two reasons:
1. We live in a post - Stanislavkian era; a time during which the concept that there is a correct method of acting came to the fore, and that it can be taught. Prior to this, it was often assumed that, if you could act, well, it was just because you intuited how to do it, and 'ordinary people' could not be privy to these arcane secrets. But Stanislavski said, I can take anybody, and teach them how to be a better actor. His methods became absolutely enshrined in the USA, and all sorts of rival schools teaching, basically, variations on the 'system' that would create the 'ideal' actor, emerged. For a long time, this country resisted such innovation, but, in the end, resistance crumbled, and now, we too are trying to ensure that we can turn out 'systematic' actors. This seems to have led to a proliferation of courses, and schools.
2. A combined set of factors: a) The acting profession is now overcrowded with actors - partly because of the loss of the 'closed shop', partly thanks to the proliferation of drama schools and increase of graduates, partly because of the current obsession with fame/celebrity etc. leading all and sundry to think they can be an actor, and, indeed, for some of them to get employed acting (with no discernible talent for it!) etc.
b) Casting directors, agents still require criteria to sift wheat from chaff (in fact, more so than in the days when there were less actors on the markets). Again, their choices can no longer be made with reference to the Equity 'mark of approval' (because Equity has lost 'closed shop' status), nor to the honing of a talent that comes through working in rep and so on. So, what they often fall back on is the criteria of: has the actor been to a well respected drama school, or not?
Beyond that, it's safe to say that there is no tradition of actors historically ever doing anything other than learning 'on the job' - how did Shakespeare's company become good actors? How did a Commedia troupe become good actors? They learnt from their peers, they picked up on what worked for their audiences and what didn't; etc. etc. In other words, they trained themselves. And, of course, all decent actors ultimately have to train themselves - they have to learn what 'performance tricks' work for them, and how best to utilise them to their advantage. No one, historically, was setting themselves up as self - proclaimed arbiters of the 'right' and the 'wrong' ways of being an actor. I'm not saying there weren't 'right' and 'wrong' ways in Elizabethan times - simply that, if you were doing too much wrong, I suspect you'd, at the least, run the risk of getting booed off stage, so it was necessary for you to learn how to *get things right* sooner rather than later.
One of my tutors at drama school used to say that, in his opinion, the only reason we, as students, were at drama school today was because there was no rep left extant in which we could learn everything that the teachers try and cram into a year - and he regretted the fact.
So, basically, this insistence on being 'trained' is, I'm afraid, a sign of the times....even thought most actors worth their salt know that, if you're good, it doesn't matter how or where you learnt to perform and deliver.