Twitch chat is IRC compatible, not compliant, meaning there’s connectivity for traditional IRC clients but it’s not always going to follow the IRC spec, and implements functionality based on the needs of the site rather than ensuring all new features can be supported by old IRC clients.
Joining a channel should be relatively quick, it’s just that the notifications for joins sent on TMI are batched (and not sent at all for channels over 1,000 users). Things like channel list are also cached, just like every other API endpoint, so some delay as to when that list will be updated is expected.