Basically, all it costs you is trade routes, and the positive laws the UP may have passed (free weapons on transports, speed on constructors, etc).
The only up side is getting out of the crappy laws - starbase module limit, delay at start of war, war tax, tax on starbases/planets in other people's influence, etc. There are quite a few scenarios where trade simply can't cover the expenses of staying in the UP.
I consider the ship-moving one to be the most powerful POSITIVE law they can pass - it's an instant AI killer. They can't plan ahead for it, you can. It automatically moves all the AI's ships into easily ambushed positions, and clears out all their mobile defenses, leaving your transports a free run (once you've cleared the orbiting ships). I guess that's the advantage of running a very influence-heavy empire, I never have a war in anyone else's territory. Even if I don't have any planets nearby, it's still my territory. More than once I've made peace and declared war again to bump their ships back to where the new border is