No. or rather, I don't want cool spells and variant casting systems to be monopolized by these classes at the expense of the regular mage. For example I really dislike Vancian and prefer spell-points but I don't particularly care for psionics. the new approach lets me pick and chose the theme and main mechanic for every type of mage.
I imagine variant systems don't need to be exclusive and all casters could have access to them but without this kind of niche protection or a really different spell list to set them apart from the Mage, the other classes would have to be very different in other aspects. A lot more than they were in 3e.
This is especially true for the Sorcerer. I don't think being just a bit less squishy and having a couple of variant minor class features is enough to justify a whole separate class. The bloodline fluff can easily added to a Mage tradition and things like potions and scrolls can be replaced without changing the base class dynamic (do we know that every subclass is meant to have them?)
The others may be trickier but the Warlock's "scary" stuff shouldn't be too hard to implement as spells (it would make sense too) and, I admit this is a bold change but, to me a "mind mage" Psion will better fit in default D&D than the whole "arbitrary combination of 19th century pseudoscience + Asian mysticism + New Age crystals that looks very much like magic but really isn't".
The obvious advantage of combining them all is that it avoids a lot of redundancies. Do we need, for example, an elementalist school, an elemental bloodline and an elemental pact? If not, which class is going to get the elemental theme?
As for multiclassing, these subclasses already use the same spells and it shouldn't be too hard to give access to other features at some point... or do people really want to mix different spell progressions and casting methods?
Now I don't mind these classes being separate if they become truly different, something along the lines of the first Sorcerer and Warlock previews or better, an actual gish but again, I don't want spontaneous spellcasting primarily associated to them while the Mage is stuck with Vancian and some obscure, barely supported variant thrown in the DMG. At least if the Mage is supposed to cover all these classes, there's hope the non-Vancian options will get proper treatment.
But as always, the devil is in the details.