Pinotage said:
Why do you say it's powerfully broken? You can only use is 1/day - I don't think that's broken at all. It's a feat that provides good versatility for the wizard who can leave a spell slot open and cast what's needed even if he doesn't have the spell prepared. It's a good utility feat. Hardly broken unless I'm missing something. Even the 1 round thing is not such a big deal 1/day.
Pinotage
The Wizard's got a list of big limitations:
1) Spellbook dependency
2) Foreknowledge Requirements
3) Limited Spells per day
Now, many Wizards will deal with 3 by way of Crafting wands and scrolls. 1 almost never comes up, as the DM invoking it pretty much completely neuters the character, which is no fun for anyone at the table. With 2, most wizards deal either with divinations (this will not work when: a) The DM doesn't plan that far ahead, b) the DM puts countermeasures in place, c) you're not high enough level to use the better ones) or with a generic spell list that will at least be useful against most critters.
Alacritous Cogitation will deal with both 1 and 2 to an extent - if you're caught without your spellbook for whatever reason, you can still pull any spell from it to cast (once). This will generally be an escape spell of some nature, but not always. You take it at 1st level when you don't qualify for all that many feats, and later on at 17th, you can Gate out of prison using it. That doesn't work with Spell Mastery, as you have to keep taking it for it to keep up (or retraining it, if you're using that particular book). It deals with 2 by combining a generic list (or a divination-inspired list) with a top-level spell that's left blank. When you run across something you're not totally prepared for, you can have "the perfect spell" available in a jiffy.
Compare to the Mage of the Arcane Order PrC - this one feat covers roughly 80 or 90 % of the PrC's biggest class feature (the spellpool), and does it faster (one full-round action to cast the spell with Alacritous Cogitation, vs. one round to call and a standard action (in most cases) to cast from the Spellpool) with less cost (no spellpool debt, no dues, no quest requirements, no focus requirements, and you can still take other PrC's and reap all the benefits). Alacritous Cogitation's only real requirement is that you have it in your spellbook.
Plus at low levels it gets rid of the big "Hit me! Hit me! I'm casting a big spell!" sign on a low-level Wizard casting Sleep or Enlarge person while it's everyone else's turn.