I have my browser setup in a way that makes Cloudflare quite intrusive. I use the Temporary Containers extension on Firefox to open almost all websites in temporary containers (paired with the Containerise extension to whitelist the handful of sites that I like to stay logged in to).
About 30% of the random (like from web searches) sites I visit throw the Cloudflare captcha at me...EVERY SINGLE TIME. I'm so sick of picking out boats and buses that I just close out the tab without bothering the visit site.
I assume, that if I wasn't using Temporary Containers, a Cloudflare cookie after the 1st captcha would persist for the entire browser session, but there are privacy implications which are beyond the scope of this post.
Anyways, I guess what I'm saying is...Cloudflare sure seems great. Dangerously great.