Wow
Looking statistically, it seems fair because of the fact that a typical wizard will get four spells at every two levels of spells, right?
...But what about those who will go out of their way to get every spell, something that a sorcerer can't do?
I suppose it's almost fair if you're giving sorcerers all of the metamagic feats. If I were you, I would give sorcerers a few extra spells, maybe one every third or fourth level, which were at their highest level of spells and moved up when they leveled. That is to say, it's fair for these two classes, maybe not for all classes.
There are other serious problems with this variant as well. On the one hand, it works great if you have a bunch of fireball chuckers who'll go through life as though life one dungeon after another, as though it were a game of hack&slash. But on the other hand, the only reason that I (as a wizard player) will not prepare modenkainen's magnificent mansion every day is because I know that it's taking a spell out of my four. I'll always have it there, rotting in my spellbook, but if I know that at the end of the day, I'm going to need that mansion, maybe with a watchdog guarding it, I get to prepare for that.
Also, how do the spells Rary's Mnemonic Enhancer and Mordenkainen's Lubrication work with this? Because I know that if I were a sorcerer fighting one of your wizards, I would wait until I saw him use a spell to work against him on it, but then he has lubrication and uses it again without my even being aware that it's back in his mind.
I can only hope that the cleric, paladin, and bard get something similarly powerful, which would be hard to come up with. Druids are pretty close anyway.
Last problem: as a wizard at level one, I learn every cantrip available. That means that at 1st level I will be able to cast (ready for this?) 22-23, based on Intelligence, spells every day. By the time that I hit level twenty, this hasn't even tripled if I haven't been going out of my way to learn spells. The sorcerer, known for the massive amount of spell chunking and the damage he will cause, gets eight, and by level twenty, has fifty four. This is of course still not up to par with the staggering sixty three that my Wizard can cast by this point. Of course, if I were told this was happening to me, I would wait until I hit level seventeen and just start wishing for various spells until I know all of them. Hell, even if I don't wish for spellbooks and just wish for scrolls, I'm only limited by the amount of monsters that I can kill in one day. I just have to get 5000 every day, and a little trip to an elemental plane should get me that. If I run into a problem, I just have a plane shift on contingency (I can make one a day, not to mention a gate to get in and various means to avoid the energy damage). If I'm not quite up to my quota, I'll use planar bindings to bring in enough to fill it. Hell, the worst that can happen is that I don't get 5000 exp that day. So I don't get 365 spells that year. I'll live knowing that my meteor swarms (sorry, swarm) will kill entire races of people on the planes of Ice and Snow some other day. A little evil? Not if I make sure to go after every denizen of the Abyss, every creature of every minor Hell, and every every demon, devil, and red dragon to ever test my wrath. A little fascism? Why yes, thank you. Do you have honey to go with that?
I'm not saying it's that bad. If you were my DM, I would smile, nod, and say, "Yeah, that sounds like a great idea. It's really innovative." And then, I'd go home and have happy dreams of... well, of what I've just described. Honestly, I love the idea and I think it will enrich the gameplay in your circle. But be prepared to send Gods after your players if they have the minds for it. Be prepared for them to win. Be prepared to prepare every game with the intent of testing your players. Just think about the ramifications upon the rest of the game, and if you're willing to go through with it, then I think you're going to have a great time.