So bitcoin private keys are so long that they cant be guessed.
Once register on a site like AB, couldnt it autosend us an encrypted msg with a custom url with a long ass hash in it that would give us either a temporary or dedicated custom url we could use to log in with no password or captcha?
Would there be some risk in this?
There could be some hypothetical risks, but I think that since the CAPTCHA system is doing fine, there would be no reason to incorporate any new type of system such as you're suggesting.
A risk off the top of my head would be that it would be easier to phish people as there would be no more single dedicated link, and hundreds of people get phished a day as it is without adding custom URLs.
I understand that these are annoying, but just refresh the page until you get one you know you'll successfully fill & life will become less stressful.