My son actually asked to play Dungeons & Dragons with me today. He's still 4 months shy of his 6th birthday, so of course I had to do a fair amount of simplifying for him, but I ran him through the CYOA dungeon from the Mentzer Basic Players Manual (killing two birds with one stone, as that helps me prepare for the Cover to Cover post).
At first, he wanted to play a "wizard" so we rolled him up a Magic-User. I briefly explained spells, and gave him Read Magic plus let him choose three more (one more standard, plus one for each point of Int bonus he had). He chose Hold Portal, Light/Darkness and Ventriloquism.
Rather than explain the intricacies of Vancian spellcasting to him, I figured I'd just let him cast each spell once during the adventure, and let him return to town and rest up if he wanted to refresh them. Turns out he died before he had a chance to cast a single spell, although he did take out a rust monster with the help of my wife's old Halfling PC from our gaming attempts from before our son was born (her Halfling is level 4 with a displacer cloak, +1 short sword, and a few other nice things). Anyway, goblins then made short work of our wizard, who had a 6 Constitution so only 2 hit points.
My son rolled up a Fighter and, with the help of Blossom the Halfling for combats (my wife was reading a book at the time, taking breaks to roll some dice when necessary), went on to trounce the dungeon, getting all the loot, dividing it with Blossom, then getting it all doubled by the magic mouth.
Back to the idea that hit me. Since I was going to let him use each of the 4 spells in his spellbook once each, I got to thinking. What if, instead of preparing spells, a Magic-User, Elf or Cleric (Clerics will need spellbooks or prayer books or something in this version to make it work rather than access to all their spells) can cast each spell in their spellbook a number of times per day equal to their Vancian spell limits?
So a 1st level M-U can cast each spell in his/her book once per day (as above). At 3rd level, with two 1st level and one 2nd level spells per day, each 1st level spell in the book could be cast twice, while each 2nd level spell could only be cast once.
Of course, 3E style limits of up to 4 per level per day might be a good idea, and my Level 15 cap instead of the BECMI level 36 cap would be necessary to prevent abuse.
What are the benefits? Well, first of all a lot of the utility spells that rarely see play would see play. Spell-casters move away from the tactical nuke/heal-bot mentality they engender. Yes, as they gain lots of levels they can do that, but they would still have lots of utility magic to go around as well. Gets rid of the "I cast one spell and am then useless" complaints of low level play. Makes caster characters' main motivation to seek out magical books, libraries, or other casters in order to expand their repertoire.
Drawbacks? All those arguments about casters replacing Thieves become more tenable. If you can cast Knock or Locate Traps several times a day without having to give up other (attack/heal) spells, might as well magic your way through such things than rely on a Thief's percentage chances. Maybe in an OD&D/S&W game without the Thief this variant would work better.
This is not an idea I'd want to use all the time, but for certain campaigns (or maybe as a replacement of the caster roll mechanic I'm using in Chanbara?) it could be fun.