If that is done then believe me some people will take the advantage and launch DOS attack on the forum which will make it difficult for people to access the forum, so the captchas is a way to protect the forum from attack.
The solution you can use is to check the login forever box, which will keep you logged in for a long time.
If you implement such a service, it must be tied to a specific Ip address, otherwise you are right, it is a threat to DOS attacks. But given that in most cases, each Internet user 1 ip address, the attack is extremely impossible.As for the Tor, it is an anonymous browser, with the substitution of partial or full of your Ip address, so you have a problem with the captcha. Alas, I have not met such services that you offer.