@Alb087 You do not have to (nor should you) use the default matrix.org, and there are other homeservers that do not require reCaptcha; see https://servers.joinmatrix.org .
Anyways. reCaptcha is specified in the Matrix spec, likely considering it being the “most popular” choice. However, since Matrix is moving authentication to OIDC (see https://areweoidcyet.com ), which further allows homeservers to customize their registration flow, the specification will eventually be made obsolete.
This list (which I run) checks whether listed servers are open or not. As for communities, they are not dependent on homeservers (minus the abusive ones), you can find rooms to join through https://matrixrooms.info and join them with your account on any reasonable homeserver. As for slowness, refer to the physical locations of each server; additionally see User Guide (in header) for a list of the most used servers. However, do keep in mind that resources and experience of each server differs.