Prestige Classes are fun for the players. Simple.
People tend to let the whole X/X/X/X/X thing on their Class entries for their character sheets grate on their nerves. I say don't let the damn three or four titled character do so. It's just a few names mashed together, when in your campaign world the character may be a new brand of "class" or warrior or possibly a type of spellcaster banned for ages (or looked up to). Put in parentheses your own class name and enjoy the darn game.
DMs who complain about broken mixes or whatever, shut up and deal. A proper DM would make use of it with his NPCs and PC's antagonists. I do all the time. My motto is always "You can have your 50 Strength, my baddies will just have 150 to match the challenge".
As for the ones that say the concept doesn't fit in your world, fine. But if a player wants to play, it's the DMs right to make it work in the campaign. The multiverse is infinite, I'm sure every DM's world has planes of existence, the character can come from beyond if that Warlock dwarf really won't fit at all in your world. He's a dwarf from another world, possibly. Whatever works. It's about the player, not the DM, and let them have their game.
So, yeah, my feelings and rant on the prestige class thing. I love them, personally. Makes characters unique from one another and brings life to a game. My player has a Samurai/Psychic Warrior/Elocator, but in-game he's "A samurai of Clan Kaisetsu who received the "gift" upon his maturation and has mastered a particular style of fighting carried within his family's clan for decades. His mind opened up to a specific path for his mind, gearing him towards a hyperawareness of space and time and he combines this with the Kaisetsu Style."
That's what he sees, and what I as the DM sees too.