>Clearly, if this happened IRL, people would just put a limit on the number of masked people entering that bar until there wasn't a group of 1000 of them trying to get in.
IRL, the bar would call the police and anti-riot forces would move in with crowd control equipment. Tear gass would be launced at the masked people and a lot of the masked people would be hauled to the police station where their identity would be recorded and a background check would be performed. It's not pretty but it's reasonable.
I have used Tor out of a legitimate wish for privacy. I have cursed Cloudflare and Google in passing to myself for their captchas presented to me when I've browsed through Tor.
Captchas in general are a royal pain in the butt, but they are among the most effective at protecting sites from abuse, so even though they annoy me at times, I hold the view that they are a net positive.
If you want to help preserve anonymity, I think the best course of action is not to focus on Clouflare, but instead to help maintain one or more communities on onion sites. The change must come from within. Once it has been shown that an onion site is able to provide useful services over time with privacy but with the same level of protection from abuse and bad people, then, in my view, it is time to reach out and educate the wider 'net on how this can be done.