For me, the thing that would make a Prestige Class worthwhile is if it were truly Prestigious. Like, the Archmage example is good, because you can't just be an Archmage at 1st level. Similarly, things like High Priest, Guildmaster, Grand Champion, and cough Warlord seem like they should be reserved for higher levels.
WRT Warlord--let's not go down that road. People have
extremely entrenched feelings. I am 110% in the "Warlord deserves to exist at level 1" and that's not going to change over the course of this thread. I am willing to respect that you and others don't feel that way, let's not utterly derail yet another thread with that.
I can see this as a good thing, but I also feel like there's another place it can fit in--that is, the
path to Prestige. AKA 4e's idea of both Paragon Paths and Epic Destinies, which are more about a destination than a starting point. Prestige Classes might require you to start off prestigious, or they might be about concretely demonstrating the process of achieving Prestige.
However, for all of these, the question is: Do you need the full mechanical weight of a class or do existing mechanics cover it? Like, what's the difference between an Archmage and a high-level wizard? Or between a Warlord and a high-level fighter? Could you become a Guildmaster just by, you know, being the master of a guild, in-game? etc.
Do we "need" anything in mechanics? It's a question of satisfactory implementation of stuff. I certainly grant that it's
possible to do things as you say with zero mechanics. I also think that would be boring and samey.
I haven't written up any actual mechanics for these, so it's a little unfair to ask for me to give on-the-spot mechanical writeups for several PrCs at once. If their existence is to be justified at all, those mechanics should have care and thought put into them, not simply throwing something together off-the-cuff. However, if I had to make something up with literally zero prior work, it would be:
Archmage = Unlocking universal rules of magic (e.g. stuff that crosses class boundaries) by exchanging a portion of what they already know.
High Priest = Expanded domain access. Deities rarely have a single domain; a high priest ought to represent multiple facets of their deity.
Guildmaster = Assuming this is specifically a
thieves' guild thing, Contacts. An eyes-and-ears network can by itself be a defining feature...for the right campaign.
Grand Champion = No idea, the title is so generic I'm suffering from Tyranny of the Empty Page.
The main difference between a miniclass and a prestige class is, a miniclass lacks prerequisites.
Then no, I'm not talking about "miniclasses" in this sense. I am explicitly talking about things with reasonable, appropriate requirements that develop your skills in a different direction than they would be if you stuck with your normal class.
So, the Vampire PrC might require a minimum Charisma (vampire magic is akin to sorcerer's, being ah..."in the blood" so to speak!), having been bitten by a vampire and not been treated, and undergoing a ritual to focus and empower the transformation. The Werewolf PrC might require minimum Strength, proficiency with Nature (to reflect tapping into your 'wild side'), and a moonlight vigil. Again, simple and straightforward things. Stuff that requires
at most two feats, or investing Background or class skill picks into relevant things.
No feats. No complicated build paths. Anything like
that SHOULD be implemented as a subclass, because it's the weaving together of specific mechanics. Instead, it's a short list of reasonable, achievable requirements that reflect in some sense the foundation onto which you build the PrC's features.