I hate Vancian magic

I don't like the D&D magic system. Let me rephrase that. I hate the D&D spell memorization rules. The idea that you can only memorize till you cast a spell rubs me raw, like sex on the beach.

But I think I have a simple change that will satisfy me without changing existing magic user classes.

Magic users are still limited on what spells they can memorize, but for daily casting limits, total the levels of spells memorized and that gives you how many levels of spells you can cast.

For example, Aloysius Archmage, a 3rd level magic user, can memorize two 1st level spells and a 2nd level spell, say Magic Missile, Sleep, and Invisibility. When it comes to daily casting limits, instead of being restricted to casting each of those spells once, the magic user can cast those spells in any combination as long as only four levels of spells are cast. Aloysius could cast four Sleep spells, or two Invisibility spells, or one of each of his spells, or any combination that totals four levels.

This seems to be the easiest way to keep the existing D&D spell infrastructure and still be something I can get fully behind.

I'm sure someone has thought of this. How did it work? Did it destroy 'game balance'? Did it make playing magic users more fun? What were your experiences?