In theory, all the bases can be covered with four big ones:
Tank, for soaking up damage
Stealth, for sneaking around and crowd control
Blaster, for dealing massive damage
Healer, for fixing up afterwards
I have to totally disagree with the Tank, Stealth, Blaster, Healer as all-inclusive since they don't even begin to describe any of my PCs in the slightest. Its mostly because Blaster is a bad generalisation for the category into which you lump the arcane casters and psions.
If you forced me to play one of those four archetypes in your system, I would be pretty upset, and probably would not play in that system. Perhaps this is because of my preference for non-evocation wizards and psions (beguiling Enchanters and Illusionists with Cross-Class Diplomacy and Bluff, manipulative Telepaths, Conjurers who use their powers for non-combat situations [Majour Creation, Summoning creatures for non-combat purposes], secretive Diviners who have 6 Knowledge skills and know everything that's going on before anyone else [as well as the implications of current events based on the context of the last two thousand years of arcane history and the conjunctions of the outer planes]).
D&D is strong because I can play all of these archetypes if I want, very easily and without having to customise some generic class. And the best part is that I have a few ways to go about it (Do I want my enchantress to be spontaneously able to access the spells she needs but unable to have a sufficient variety of spells? Then I play a sorcerer. Do I want her instead to plan out her spells ahead of time but be capable of many different sorts of effects? Then I play a wizard. If I want real flexibility and a fresh perspective, then maybe I'll ditch the arcane aspect and play a Telepath).
That's the great thing about having all these classes: They are there for you if you want to use them, and if not, nobody is forcing you to do so. As for me, I would never play a Sorcerer because of the crippling lack of spell variety, but I'm still glad that the option is there for people who enjoy it.
I can see the point of view of people who prefer Prestige Classes to Base Classes, but I truly don't understand the people who say that they wish that all the classes would be officially removed in favour of a minute number of generic classes. If you don't like all the classes, don't use them. If you don't like the new ones coming in, ignore them. But doesn't it make sense that the availability of multiple options, even if they are not for you, is a good thing in general?
If we go to a generic/advanced/prestige system, there will be a lot of "No you can't do that" moments, where the DM has to say, "I'm sorry, you can't play the character concept you want until you qualify for an Advanced Class. Your Monk-like PC is just going to have to settle for being an Expert with the exact same abilities as Bob's Assassin-like PC and Jenny's Bard-like PC [except for specific skill/feat selection, but they use the same list for the feats, have the same weapon and armour proficiencies, etc]. In my opinion, it makes characters more bland and boring, and less fun to play. Isn't it more fun to say, "Yes. Bob can play a Roguish Assassin-type character who sneaks about and attacks distracted enemies [can't get Sneak Attack until advanced class using the Expert class], you can be an unarmed and unarmoured combatant who fights with discipline [sure, you could try doing this by selecting Improved Unarmed Strike, etc as your feats and voluntarily removing your armour, but then you'd die because the Expert's abilities are far fewer than what the Monk gets to compensate their unarmed, unarmoured style], and Jenny can be a silver-tongued Bard with plenty of random knowledge and the ability to raise the morale of her allies with inspiring performances.