Initiative vs. Reaction

The real beauty of Apocalypse World, and the thing that has most changed my outlook, is that there's no initiative. Since the GM never rolls dice but only reacts to players' rolls, initiative is a non-entity. If somebody declares they want to do something, they simply do it, unless asked to roll for it. Then they either succeed and do it, partially succeed and get a little fuckery on the side, or they fail and the GM gets to make their own move against the PC. There's no binary of succeed/failure. I may actually adopt this GMing technique for every game I run from now on, because now I can't shake the feeling that initiative is a cudgel used to parse the story into a sequence of actions that don't really make any sense.

The "GM only reacts to rolls" style would seem to massage what a player wants to do with their character as well. If a player wanted to attack somebody and the GM called for initiative, what would happen if he rolled the lowest? An entire turn of combat would happen around him in reaction to an attack he had yet to make. The narrative of the story is now forced into "Everybody could tell Baker was about to attack Gogol, and so everybody started shooting around Baker, leaving him and his gun useless." when the story should be "Baker pulled his gun and shot Gogol in the face, and that's when all hell broke loose..."