That's up to the site owner.
For example I configured my osdev wiki (mediawiki based) so that the history and other special pages get the Cloudflare test but just viewing a page doesn't trigger it. OpenAI and other bots were generating way too much traffic to pages they don't need.
Blame the bots that are DDOS'ing sites for the captchas.
Wait a minute, DDoSing is illegal, how come OpenAI et al. haven't gotten sued to the ground yet ??