It depends. Fortunately, Rydel gave us 2 choices in RSE, and these bikes are meant as check and balance to the other.
For Mach it is as the others have mentioned above is for that time attack record on the cycling road, as well as for running past those muddy slopes, and for getting to rayquaza in the sky pillar. However, story-wise, I don't think one should use the acro if their purpose is to simply complete the e4.
Acro (slower, but enables hops, bunny hops) is as also mentioned is for some more interesting secret base spots, bunny hops are useful for encountering wild pokemon while not wasting safari zone steps (with the absence of sweet scent in safari zone, it makes turning obsolete) and also for getting to other places in the emerald safari zone (note that mach bike can be used in the safari zone as well due to the presence of slopes though they give you two different routes of the safari zone iirc).