I thought Time was the straight main to the chain's shenanigans but in reality he used to be just like them and so doesn't personally see anything really wrong with their behaviour.
However where he's matured into simply acknowledging the outsider 'normal' view, Warriors internalised it before even donning the hero's scarf and has always been too conscious of how he's perceived.
I think I've said it before but Warriors didn't have a traditional adventure like the others, cities and towns aren't just pitstops for him so he respects infrastructure and social decorum. Plus he's used to minding his reputation and maintaining his perfect image. Whereas most of the others had the freedom to act pretty much like cryptids, showing up out of nowhere, spawning local legends and then disappearing after doing only slightly more good than harm.
Even without that pressure Warriors is still holding himself to that standard and even extended it over the others. Had they actually done something weird Time would've have called them out on it, but he didn't in this case because a bit of parkour is like...fine? It's really not that big a deal. They didn't break anything. I just find this aspect of the Captain's character interesting.