I think it would be better to increase the movement speed of everything instead of what the OP suggested to be honest.
So that enemies can still catch up to you and hurt you (Or they could even increase the speed of enemies attacks slightly too if them not being able to hit you is still an issue). The OP's suggestion leads to the possibility the buff doesn't end before running into a new set of enemies.
Either way it's an exaggeration to say a movement speed increase would completely change the game. It wouldn't make it like pso2, because there's much bigger changes over simple movement speed increases in pso2. (Actually if you were to not use the new movement options for pso2, it's just as annoying to traverse maps in pso2).
It doesn't have to be a huge change in speed, just enough to make traversing the maps not so inconvenient. The movement speed in PSU is about the same in the original PSO, but PSO has enemies placed everywhere, which makes the maps not seem as bad to traverse, instead of finding a group of them far apart in large rooms in the map. If PSU's classes didn't level the way they do, it wouldn't even be an issue, because then you could just kill the first few enemies then leave the map.
But because of how they level, its more than just a minor inconvenience. The game is fun, but walking through the maps gets pretty tiring after doing it hundreds of times, especially on the bigger maps.