The least mobile right now is SCH. If you want to minimize GCD loss, you want to move with swiftcast, Biolysis and Broil + slidecast.

The most mobile is SCH, because you make your GCD roll as long as you want and move from north to south, but the cost is potency.

Every healer have their own niche when it comes to mobility.
AST will be lightspeed. Wasn't really a mobility tool so far because of the insane weave festival it was during burst.

Otherwise, even without all those tools, you can still move perfectly without dying or losing DPS most of the time.
You just have a to pause and watch cast bar.