I would encourage you to read the current literature. The evidence is more compelling than you might expect. Actually Meltzer’s 2020 paper (linked in my previous comment) touches on this exact concern under the subheading, “Getting past the Impasse”. There was another good paper that broke down how the end of the Pleistocene was radically different from previous glacial transitions and how the effects of that likely played into the extinctions. Combined with the revelation that most mammoth “kill sites” were actually more likely to be scavenged… it’s not at all an unlikely picture.
Thank you for recommendations. It’s been a while since I last skipped sleep to read on these topics, so maybe it is in fact time to catch up with recent ideas. My priors are still strong on humans being ultimately responsible, especially as the entire field is filled with a lot of wishful thinking about the noble nature of savage people, living in harmony with each other and environment.
I suspect it's a combination of both - climate change put the megafauna population under stress, and then humans showed up and dramatically exacerbated their woes.
The extinction of moa in New Zealand is entirely attributable to over-exploitation by humans. The extinction of megafauna in Australia seems to have been climate change + human hunting + human modification of the environment. https://en.wikipedia.org/wiki/Fire-stick_farming