That actually used to be the case (circa 2008) with shattered haven. The problem is, the times when you want to walk are very few and far between (zombies, right?); and even in ff6 you could choose a setting that made sprint boots default to on, which I know I used. With keyboards, many can only register three keys at once, so holding two directions (if you're moving diagonally) plus run plus attack would not register the attack!
Lastly it changes he balance if you don't know to run. If you walk and the grays are inexplicably fast and you die, that's bad. That used to happen a lot (circa summer 2008, when Lars was giving me much feedback). On the other hand if you are balances for walking against the grays, but you have essentially a turbo button, suddenly they go from menacing to a joke. That also happened around that time. I had tried doing stuff like he boots in Zelda 3 or sprinting in secret of mana, but none of that panned out. Ultimately the current design was arrives at, and then when the overworlds got really large we started having that be faster movement than the levels. I think that last one was one bridge too far.