@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.
@Blaze matrix.org indeed is slow at times. You should consider moving to other homeservers: https://servers.joinmatrix.org
@shortwavesurfer @Blaze Were you on monero.social? I'm aware that matrix.org's Cloudflare firewall may be blocking random homeservers from directly federating with it.
@Draconic_NEO @frosty Well, you can have multiple accounts on the same power level.
matrix.org is not that good for long-term usage due to performance issues (it's slow) and, well, centralisation. You can see https://servers.joinmatrix.org for other choices (most of them are quite stable).
@frosty @Draconic_NEO A room does not belong to a specific server: unlike XMPP, a room is copied onto every server that has at least 1 member in it. So as long as there is at least one member from matrix.org, the room is technically on matrix.org.
If you're talking about room aliases, then you can have many aliases on different servers. The main alias is mostly cosmetic though (as long as that server is reliable).
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.