I've heard that "acceleration is small and therefore insignificant" claim before, but I'm not convinced it is wholly accurate.

Yes, accelerations are low in bicycling, relative to a motor vehicle. But does that make them insignificant? I would think that acceleration is quite important to a track cyclist doing a standing start 250, or a road cyclist attacking on a steep climb, or the attacked cyclist trying to bridge back. Having attacked--and having been attacked--many times, I can say that getting up to speed quickly is pretty important for getting a gap.

A standing start track sprinter goes from 0-15 m/s in about 150 meters.