The "Core Four" are good enough; everything else can be represented by the right combinations of themes and backgrounds layered on top.
Not if the Core Four wizard is a Vancian* caster, they're not! I am seriously freaking tired of having all arcane casters shoved into the box of that stupid, stupid mechanic. 3E was the only edition that gave us other options, and it's the one thing I really love about 3E. I accept that there are those who love the Vancian wizard, and by all means 5E should support those people. But I am not one of them and
hate being forced to use their system if I want to play an arcanist.
And I don't see any indication that the wizard class will have a non-Vancian option in 5E. I don't really see how it could--it's not like Vancian casting is a little fillip on top of the class, it's built into it right down to the core. A theme that stripped away Vancian casting would require gutting the class to such an extent that you might as well just make a new class anyway. So give us the sorceror and the warlock and leave it at that. Vance-lovers are happy. Vance-haters are happy. It's all good.
Then, once you finish up with the arcanists, there are psions (don't like psionics myself, but it is very definitely Its Own Thing); monks (sorta fighters, sorta rogues, sorta clerics, not really any of the above); and bards, as you yourself point out. There are probably a few other oddballs I'm forgetting right now.
[SIZE=-2]*Clarification: By "Vancian," I mean that they rely heavily on fire-and-forget abilities, where each ability is like a grenade. You throw it and then it's gone, and you can't use it again until you rest and restock your grenades. In classic 4E,
every class is Vancian. Essentials made it possible to play a mostly non-Vancian fighter or rogue, but wizards were still stuck with it.[/SIZE]