The increase in movement speed can be really helpful. It helps a monk connect strikes against moving targets since it keeps you in range whilst the animation is running. Other melee classes will need much better timing with their movement in order to maintain proper distance to connect their attacks in the same situation.

I do agree that FoW helps a little when dodging AoE as well. A good monk should cycle fists as the nature of the encounter changes. Unlike the bard song, FoW can be maintained in combat.