I'm not opposed to their never being any sort of official prestige classes in 5th edition. Their used to be two basic sorts of prestige classes - those that were mechanical in purpose, and those that hung in-character organizational association on mechanics - and both of those can be handled by other means in 5th edition. The mechanical sort of prestige classes can have their purpose delivered by a sub-class or a feat. The organizational association sort of prestige classes can have their purpose delivered by a background, a feat, or special options of features like maneuvers or spells that have a "members only" gate to them, if not being handled entirely by role-play.
That said, I'm not actually opposed to the prestige classes that got included in the 5th edition version of Onyx Path/Nocturnal's Scarred Lands Players Guide, because they stuck with 5th edition style presentation by labeling them as optional, and delivered them in a way that I feel is closer to "super feats" that you have to trade up 2-5 levels of items on your class feature list in order to gain the full effects of, than it is to actual classes. I figure, though, that I'll allow my players the option to take them and will basically never see anyone choose to do so, just like my group have not chosen to engage in multi-classing.