It's not because spells are an ability, rather than a resource, that you use the same spells all the time. The way I see it, you would be limited in the spells you cast not by the spells you memorized in the morning, but by a resource used to cast the spells (mana, fatigue, whatever). You could still learn new spells with scrolls and books, maybe they'd have a level requirement, or a skill requirement if there's a skill system (then there could be just one skill for magic, several skills each representing a specific magic school). You would be able to more or less spam Magic Missile, instead of relying on that sling (the D&D4e wizard has at-will spells that aren't cantrips, and Magic Missile is one of them ; it doesn't scale up with level as much as the old MM did, but it's better than a sling) and maybe throw a bigger spell or two if it's a tough fight. And then after the fight, after resting a bit, you would still be able to cast a couple of utility spells in order to help the party with that door the thief can't open, without having to rest first.
What I know for sure is that while playing a wizard in BG/BG2, I ended up always memorizing the same damage and control spells all the time, because I spent most of my time fighting things in dungeons. It doesn't matter how many spells you know, if the moment it would be nice to use them, you don't have them ready. I prefered sorcerers to wizards in d&d3 just for that reason : the sorcerer did not know many spells, but he had them ready all, all the time, so in the end you ended up knowing one or two combat spell for each level, and the rest could be utilities that you had at hand the moment you happened needing them.