Well, I don't see the idea as being exactly equivalent to Prestige Classes. I see it more like this:
1) When you level, the most fundamental choice you make is what class to take the next level in. Every other option flows from there. (Assuming multiclass is allowed, of course.)
2) Right now, you have 12 options as to where to put that level. (More if homebrew is allowed.)
3) More options are fun, so what if I had more options as to what to do with that level choice?
4) You can add new classes, but that has a lot of design overhead and must support a thematic concept with room for subclasses going from 1-20. That design space is limited.
5) 5e's math is based on hit points and proficencies increasing with level, so simply trading in a level for another option isn't feasible. Any new silo for level benefits must grant hit points and a Hit Die, and must count towards overall character level.
6) Based on 4 and 5, the concept of a class with limited scope becomes appealing. Allows for more options, but less design overhead. 1-20 progression is not required, as is room for subclasses. Modular options within a design chassis already meant to encourage modularity would be redundant (although not poor design, just not required).
A class with limited scope, that isn't level 1-20, and lacks subclasses.
That is
literally the definition of a Prestige Class.
My point was that 5e is designed with story in mind. So the Prestige Classes would be story based and narrow enough to fill the voids that do not make for good subclasses. They would be the "classes" that do not work as level 1 options. Like the archmage or elite knight. But while said Prestige Classes might not have
mechanical prerequisites, that type of class would almost certainly have
story requirements.
What you're asking for sounds like Prestige Classes divorced from story. New mini-classes that exist solely to provide new options and mechanics. New options for the sake of options. Which isn't how the design team is adding options to the game.
Adding new options just for mechanical benefits doesn't improve gameplay at the table. The opposite really. More options are fun... away from the table. Between games. But that fun typically comes at the expense of fun
during the game.
The catch is perfect balance is impossible, so when you add new options, some are going to be better than the baseline and some are going to be worse. If you add a dozen new options, there will be three that are just outright
better. Option creep = power creep. So if you add a bunch of new mechanical Prestige Classes that's just outright increasing the power of characters, destabilising the balance at the table and negatively impacting play.
That's exactly why feats are easily the most disruptive part of the game's balance: they're a list of a couple dozen modular options people can use to maximise their effectiveness, where you can pick the very best ones and ignore the weak choices.
Each decision point in classes is a point of variance in terms of power level. A place where a character can be above or below the norm, And when you can have not one but a dozen points of variance in a single class, that creates a wide gulf of power levels between characters. That's when expected power level and encounter design falls apart. That's what breaks games.
Ask yourself this: would the prestige class options be as fun if the class options were entirely out-of-combat bonuses? Exploration features and ribbons? Theoretically they should be as fun: it's more options, right?
Probably not. Because it's not just about more options: it's about picking the
best option from the options. Which means it's inherently about breaking the game's balance.