Setting, organization or even adventure-specific PrCs would be one of the best uses 5e could put them to. They don't bloat the Standard Game, they're just there to provide a PC connection to the material, when you're done with the material, you're done with the PrC.
I disagree, Tony, with respect.
Here's the problem - good PrCs have their own mechanics. Those mechanics take a lot of work to create, and to ensure they are balanced and workable. The example PrC for 5E is a great example - the effort involved there is pretty huge.
If a PrC doesn't need it's own mechanics, it shouldn't be a PrC, I would suggest. It should be an in-game organisation, which may well have significant temporal benefits, but which doesn't have mechanics. The Knights of Awesome Knightlyness, who are all/mainly Paladins don't need a PrC unless they, by design, must depart significantly from the default Paladin class.
The Purple Dragons in the FR are good example of a group who absolutely have no need whatsoever for a PrC, yet will almost certainly get one. They're pretty much all Fighters or Mages. The power their organisation has is entirely temporal, and is in no way magic or mystical. You are not changed on a basic level by becoming a Dragon. So they shouldn't have a PrC. There's literally no reason.
Thus we have dichotomy - either a PrC has mechanics, justifying it's existence, but the cost of creating those mechanics suggests it may need to be more broadly applicable, OR a PrC doesn't have mechanics, and should not be a PrC.
There will be exceptions - Dragonlance's knightly orders do change you significantly in joining, will have their own mechanics, and it matters to the setting that they do, so should be PrCs, for example.
But mark my words, if you don't like PrC proliferation, the whole path of setting-specific, organisation-specific PrCs as a normal, common thing is a really bad one. As I've pointed out, at best it means a ton of needless PrCs which replicate each other (sometimes even within a setting), and even if they're technically not applicable to other material, that's still proliferation of a kind. At worst it means a lot of unique/cool mechanics being generated that are almost never used, which is a huge waste of game-designer time.
So I think what must be avoided is ASSUMPTION that because an elite organisation exists, it warrants a PrC, or, gods help us, multiple PrCs.
EDIT - Also, to make a subtext, text, there's an element among game designers, one I've never seen avoided, of "Keeping Up with the Joneses", and/or "Lowering the threshold", which is that if even non-mechanically-different organisations are warranting PrCs, then virtually every organisation warrants one, which leads directly to a 3.XE-type situation (most 3.XE PrCs were precisely that). If that caused bloat in 3E, it'll cause bloat in 5E.