It may be related to the country concerned in the question.
I've done some quick googling and it seems in the US, a parent needs to "own" the account.
Myself in Canada, I opened an account when I was 16; although my parents were present to sort of sign some papers, the account was in my name, and I would be responsible for any minor problems. "major" problems could not be a thing, as if it exceeded -100$ in "issues" (dept or fees, or stuff like that) my account would simply be closed and wait for my 18s.
I've found an article from the Canadian governement's website over accounting which states that in Canada, any citizen over 12 years of age are allowed to open and own a bank account.
In the US, it seems you still can, but you do not "own" it; but I havn't researched much on the US side of it, on the "how much of it you own" part.
Couldn't find "when". I havn't researched much but couldn't find when it was a thing and then wasn't; maybe it's something between states?