Aren't chetamog Animal Companions as fast as horse animal companions in difficult terrain?

[DemonicDem]

Something I don't quite get: chetamogs require you to use the support action to ignore difficult terrain, and then they can stride.

horses (or chetamogs for that matter) can just stride twice to have the same effect.

So the support benefit only seems to matter if you want your mount to step, or there is greater difficult terrain.