Why? because I have different interests and perhaps want to keep them separate but I'm still only one real person and so I'd like to be able to see and read everything from all my various servers on which I participate. Lets say I'm a gamer and I want to participate on a server specific to a game I play. I would like an account THAT server with a username of a name I use in-game. Maybe I don't want those users to follow me home. I want to play with them there and leave them there.
It seems like I have to create a completely separate account on all those servers if I want to keep them separate, but it doesn't make sense to me. The server should be able to authenticate me as a user here figure out that, sure we federate with them, and allow me to create an account with a unique username on their system. Their users don't need to know I "live" over here, only that their server trusts where I'm from.