I agree with the OP completely. I've never liked prestige classes, never played one, and never let anyone play them in games I've DM'd. If a Prestige Class is thematically significant enough, and mechanically not overbalanced, then there should be no reason why it couldn't just be designed as a core class in the first place.
I think another thing that Prestige Classes tried to fill in for were 2E Kits. People wanted a way to mechanically construct in 3E, Kits that they had in 2E. But I hated the way Prestige Classes did this. For example, if you wanted to be an Elven Bladesinger, you could start out at 1st level with the kit. It meant that you spent the 50 previous years before adventuring, doing nothing but learning to be a Bladesinger. In 3E, you didn't become a Bladesinger until you had achieved all of the required pre-requisites (something like level 7 or 8). So, all of the flavor of training for 50 years, and the "specialness" of being a Bladesinger, were nullified between 1st and whatever level. "You've been studying for the last 50 years, but until you hit 7th or 8th level, you're just another Fighter/Mage - Deal With It!".
Also, there was the balance issue of using Prestige Classes. Prestige classes added abilities you couldn't achieve through just normal Feat/Skill/Class combos gained through normal level progression. This meant that if I, as a DM, allowed someone to have a Prestige Class, I pretty much needed to encourage everyone to have one, just to keep everyone balanced. One could say that kits in 2E did this also, requiring that everyone needed to take kits, but I really don't feel that kits had nearly the impact on balance that Prestige Classes did.
This is one of my issues with 4E also, this concept that Prestige and Epic "Paths" are almost essentially required, if you want to keep up with the others in your party. It's almost like the game was designed with the "requirement" of specializing. Game concepts like this usually leave me with a very big disconnect between the mechanics of the game and the narrative aspects of the game.
If a concept is strong enough on it's own merits, then it's good enough to be a class - period. If it isn't, then it should only be modeled through options that you can learn (Feats and/or Powers). At least that's the way I see it.