"How it works: first, an accessibility user signs up at this URL, which is linked in the hCaptcha widget info page. They are given an encrypted cookie that can be used several times per day, but must be refreshed every 24 hours via login."

https://www.hcaptcha.com/accessibility

How on earth is this considered a reasonable accommodation for people with access needs? Stinks of something created with no consultation whatsoever with the accessibility community.

This is bad on so many levels, for starters that you need yet another account.