Do you realize that your version of the Wizard makes magical colleges pointless? It really destroys the traditional idea of the WIzard. The class has no mechanical way to acquire more spells/power by simple study or by collaborating with other wizards. As a result several standard fantasy tropes regarding wizards (like the magical college) simply just don't work.
Not sure if you're interested in a fix but it could be as simple as not letting spellbook access any ability but needing to colelct the abilities it has access too. This would require more book keeping though which seems to be against the spirit of the game.
I may have more later.
I admit this version is more limited. But there are still many outlets...
I imagine that a "wizard" college will include sages, elementalists, shamans, sorcerers, witches, etc. In real life, colleges serve two purposes:
-- Train new generations
-- Conduct research amongst peers
Maybe there's a third purpose too?
Anyway, the college would still serve to train new generations.
Also, since there is multiclassing, characters who are already spellcasters may mingle among their peers and learn new spells. A sage/wizard is a very nice combo, for example, as is a pathfinder/wizard.
Members of the wizard class can add new spells to their repertoire outside of their class. They can take "Diverse Dweomer", which reads: "Select 4 basic magic abilities for which you qualify drawn from any classes. You now know these abilities."
Just for this, higher level spellcasters would definitely wish to gather to learn from each other.
Wizards can take the Arcanist theme -- which seems likely for a collegiate wizard -- and select Minor Arcana and Major Arcana multiple times to reach into other classes. The theme also offers abilities like Craft Magic Item, Mana Pool, and Student of the Weave.
Perhaps an arcana college teaches and maybe even gate-keeps this theme. You might say in your campaign setting that in order to join and progress in the Arcanist theme, a character needs to join an arcane college, eldritch college, or whatnot.
As for expanding one's spellbook options, there are magic items like the Necromnicon and Astral Codex. These are spellbook-like magic items that require you study them to use them, just like a spellbook, and offer spells within them.
And of course, wizards can use scrolls, and scroll use is not limited to one's class (although reading a scroll from your class list is automatic rather than requiring an Arcana check).
Taken together, if I were a wizard in this world and someone said, "come join me at a wizard college for a while", I'd say yes. There are so many options.
All this said, it's true, it's not a 3.5/PF wizard in its extreme versatility. I would offer: A GM is free to reward a wizard character with a scroll of a new, custom-made spell, and then let the character study it and add it to his list of class spells (thus making it accessible via his Spellbook).
A new theme for spellcasters that revolves around the use of a spellbook, familiars, etc -- that allows one to become a classic spellcaster -- is also in order at some point, perhaps in the Expansion Kit!
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