The Federation is not the entire world, there were at least 4 more entities of that level who were distinct, and weren't particularly keen on joining the Federation.
Star Trek: Birth of the Federation captured this quite well in its endings representing Loss, Allied Victory, Domination ( 2/3 of the galaxy controlled) and Total Conquest.
Star Trek: Birth of the Federation captured this quite well in its endings representing Loss, Allied Victory, Domination ( 2/3 of the galaxy controlled) and Total Conquest.
https://www.youtube.com/watch?v=8A8N1N-dREc
Contrast this with the Cardassians: https://www.youtube.com/watch?v=Fy_RbUKsaj0