Speed is important for three reasons, primarily:
1) When you have the switch node (at a branch, when a squad moves over it, it flips to the other possible route), arranging your squads can control which squad goes down which path (especially useful for if a boss is on one of the paths, or you have Lilac and you want to send her squad down a web-infested path, etc.)
2) Making sure a specific squad gets to a specific point on the map first. Examples include a Toad Lily/Edelweiss combo wanting to run ahead due to the defend-against-pest + heal on pest node combo, or you want your strongest squad to reach the boss first/last, etc.
3) Especially long/short paths that are necessary to 3-medal a map (like a short route that has a pest, but goes right to the boss/flag after it, or a really long route that has a pest near the end, like 10-5)