Wiz has said a couple times that Federation overhaul is on the to-do list post Banks, up to and including the path to intergrating your federation into a single entity.
One thing I would love for a federation perk would be colonial rights; the ability to build/request a colony ship of another federation member's pops to colonize worlds that your current pops can't. No more having to find the right primitives/hostile neighbors, be Highly Adaptive, and/or spend a century doing habitability research to get the Xenophile migration fun going with those whose homeworld isn't part of your trio.
that can be achieved easily through migration treaties as it is, and far more elegantly. I would like to see a federation option to give colonization and construction access to your federation members.
What i would prefer to see is options for federation wide policies, maybe some that are by vote, and others that are things presidents can enforce unilaterally.
This, combined with an election based system, rather than a simple rotation, could lead to interesting internal federation politics.
Maybe you have to spend or auction influence to boost your chances of winning elections, maybe each pop in the federation votes, meaning if you can sway enough pops to have factional affinities with your empire, you have a better chance of winning elections.
Maybe that small 5th member of the federation has little territory or military power, but has focused on influence and ethics attraction, so after saving up influence for some years, they finally make their move, win the federation election, and use their term to push through a bunch of beneficial policies, allowing them more sway within the federation, or pushing the whole federation further in the direction they want.