I agree that most Discord users do not want to self host. However,
> Everybody will have to join everybody else’s server. Too much effort.
This is already the model. Everyone has "their own" discord server, and you have to connect to it manually via an invite. That would actually be the exact same usage.
Clicking a link (discord's approach) is very different from downloading a different piece of software and setting up a new account for each gaming group
You can connect directly to other discord users with no mutual servers. You can make chats and calls with users with no mutual servers. You can make group chats and group calls with users with no mutual servers. You can screenshare in these calls, stream to the group, etc, all just by being Discord users. No need for a server.