5e's subclasses get a bit more in the direction of a PP though, since you pick them several levels into your character's career. Not to say that they're equivalent or anything, just that it slides some in that direction. Frankly I think 5e would have benefited a lot from PPs. Maybe something slightly more flexible, like an 'overlay class' where you get one choice, you can take it at any point in a range of levels, and it just gives a bunch of 'swaps' and access, perhaps, to some kind of thematic mechanic or something. This could be very similar in execution to PPs, but would avoid the one awkwardness they had, which was "you are now an X" when suddenly the whole party's chosen path became manifest (EDs have this issue in spades).I think subclasses sit in a different conceptual and mechanical space than prestige classes and paragon paths. The former is a built-in part of your class, while the latter offer an avenue of advancement separate from your class.
I think the "it happens at a fixed level" actually would have worked FINE in AD&D, where there was no expectation of a fixed advancement of all members of a fairly stable party roster all at one time.