I didn't see the results of this immediately, but over a long game, I gradually saw how insane the influence boost was from controlling the UP. Just being elected the chairman once was enough for races like the Thalans to absorb both the Krynn and the Drengin without even trying. Next, the Iridium Corp got elected, and even though they were all the way on the other side of the map from my territory, and I had influence starbases, they started absorbing me!
Something seems to be up with how influence is calculated in general. If that's how powerful owning the UP is, I might start turning it off just so the game stays playable into the late game.