I have a bunch of publicly accessible forms and none of them have captchas.

I did once run into an issue where a signup form was abused by a spammer, but that was a simple fix (tip: in verification emails, do not include any information that the user typed in the form).

If you are careful with your forms, you don't need captchas. Captchas add a lot of friction for some users, so if they can be avoided, they should be.