[MENTION=6779993]Elderbrain[/MENTION] To be fair, there's a bit of abstraction and tweaking that's necessary with most magic-based classes in D&D to approximate a particular literary character. Actually, when I think of characters like Dresden, Harry Potter, Gandalf, and Walker Boh their magic was actually more thematically narrow than the smorgasbord of the 5e wizard.
IF you wanted a class that could choose ANY spells, you'd need to develop a way to limit its spell list to balance it against other spellcasters in 5e D&D.
One idea I've played with before (and I may come back to) is the idea of a "domain mage" who would select domains like "Dream", "Healing", "Fire", or "Chicanery." Each domain would then include its own spell list tightly constructed around its theme, along with a thematic cantrip or a minor ability of some kind. For # of domains a character knows, I'd probably use a similar progression to Warlock Invocations (topping out around 8-10).
So each mage would have their own unique spell list — constructed from each domain they selects, NOT a master class list — but allowing for the creation of a specific vision of a character without worrying about distinguishing between clerical/druidic/warlock/wizardly magic. Pretty much any PHB caster class is going to have a larger spell selection at any given moment, but with the "domain mage" you get almost exactly just the spells you want.
As a DM I like this because it encourages a more thematic approach to magic that I can easily understand. "Oh, you're playing an Air, Fire, Dream, and Light mage? Ok, that gives me a feel for the character's capabilities right away!"
However, when I tinkered with the idea, it proved to be a real design challenge making each domain have roughly equivalent # of spells on its list. In the end, I realized that given the spells in the PHB (even including the ones in EE too), some domains would just have fewer spells. So the question then became: What sorts of secondary minor abilities can be added to domains with fewer spells to make them equally attractive?
The other challenge of a "domain mage" in 5e is what sorts of sub-classes do you create for a build-your-own-caster-kit class?