Initiative as a skill makes sense because it's something which is essentially random (who happened to be in the best position to see and react to initial combat situations which are different everytime), but can be trained in to improve. This randomness fits well into the granularity of a d20 roll, as does the resulting initiative order (bigger spread of numbers means less chance of dup initiative slots, and having to stop and compare things like Dex to get the final order.)
Movement, being generally a single digit value (because you're not really dealing with feet, but squares), doesn't play as nice with a d20 roll. You'd have to establish some other value to make the check against, and how much this will increase your speed.
Let's say we use a mechanic similar to the 3E Tumble check. A successful roll against a DC 15 nets you one additional square of movement. Maybe every additional 5 by which you make the check gets you another square.
On the surface this seems fine. But if I'm playing a halfing with a base move of 4 squares, a roll of 20 or more is a 50% increase in speed. For a human it's only 33%. For a human monk or scout that already got +10 of movement from a class ability, it's only 25%. So the higher your base movement, the less of a "boost" you get from this.
Add in the fact that the higher your movement, the less likely that you'll need a roll to boost your base move. In melee, the guy with six squares of movement is much more likely to be able to get to an opponent and attack without having to boost his move. The halfling will be rolling more often. So any movement enhancing skill check becomes almost a must-have no-brainer for slower characters. Not a good thing, IMO. It also adds another die roll to the mix (I'm assuming such a check would be a free action, otherwise it'd be next to worthless), slowing down game play.
Now, I know that Star Wars rolls things like Climb and Jump into a single skill like Athletics or something, which is fine. Not everyone needs those skills on a regular basis. But movement is such a basic part of the system that tinkering with it will have quite a ripple effect, especially as one struggles to find ways to balance it.