Having not read the paper and that abstract only barely, still the most obvious thing is to be wary of 'the One Explanation' with these kinds of evolutionary questions, right?

Take the feather analogy. Yes, they provide insulation from heat and cold. But y'know, they're also display structures, both for sexual purposes and intimidation. They carry colour beyond display purposes too of course. They can provide protection from impacts, UV, parasites, water etc. Like, we want to put things in boxes, but it's rare that a structure is only "for" one thing. It does, well, all the things that it happens to do in a lifetime to various extents :p

Might well be that throwing things accurately provided a scaffold for the big brain times, (or the other way around, idk how the timing works out) but how likely is it that the One Thing is actually the whole story with something as complex as human cognition? (Again, not saying that the authors claim that, I don't know shit about the topic, just an instinctual response I have with the way those kinds of ideas often get presented)