First of all, if any of the dps mechanics is going to change for SCH, it has to be for all healers. Since that is unlikely to happen on any major scale, a lot of ideas are not going to happen.

Also, expedience is good the way it is, especialy since its not tied to anything. Combining it with a heal, mitigation, or having it compete with a dps ability (which a fairy gauge cost would), means its never going to be used for its movement.

Not just that, it breaks fight logic wise in many parts. Expedience is mitigation by making it easier to dodge, but if it can heal, does the dodge truly matter in most cases? And not just that, you technicaly never need that speed to begin with (as other jobs lack such feature and the fight also being balanced towards them). And yes, this means that while on its own it technicaly is a useless ability, when the team has a perfect play, its just as useless as plenty of other abilities. And here is the key part: teams rarely are perfect.

I think expedience would actualy be better off to also exist on the other jobs. And maybe some extra effect could be added to it that involves mitigation, but definitely not a flat 10% for x seconds. Such mitigations should rely on secondary effects instead like: only apply the 10% when away from teammates, or when far enough away from the healer, and only for a single hit instead of over time.
As in that case its purpose at least becomes clear: provide a way to spread out better and negate the incoming hit that usualy goes together with it, or when having to run from A to B, if you still werent fast enough take a bit less damage. It keeps the ability for running moments.

Unlike rescue expedience actualy has active use in a fight, even in perfect play: as it increases dps uptime for casters