Alright I got it working. Is there any way to remove the 'hold cancel to dash' thing? With the sprint shoes equipped it's just obscenely fast, and i felt like part of the challenge was fighting through areas and gaining experience.
I don't think your speed effects random encounters. I assume it's based on nr of steps. But you do get a free slot (kinda), 'cause you will be less tempted to use the sprint shoes. Besides, I think it makes more sense this way. Why wouldn't you be able to run unless you wear some kind of shoes? It's a game, I know, but still. If it's one thing JRPGs are "guilty" of, it's cherry picking realism.