Why geostationary orbit?

Solution 1:

there are antennas everywhere on the surface

That depends. When you create a new game, then you have various difficulty options. One is to play without the additional ground stations. When you do that, then you need a direct line of sight to the KSC. So you will need a satellite network in Kerbin's orbit to ensure a permanent communication link. A geostationary satellite above the KSC is a very useful asset in this game mode.

But even if you prefer to play with the additional ground stations enabled: Some people play KSP as a sandbox spaceflight simulator and not as a progression-oriented game. These players want to try everything real space programs do in the real world. Geostationary orbits are one of these things, so people want to try it too.

"ease to release payloads"

Imagine you have a mothership orbiting, say, Duna, with more than one lander. You want all these landers to land close to each other. After you brought the first lander down and then undock the next, your motherhhip will be above a different point on the surface. So you need to wait an orbit until you are in the same position again. But if you are in a geosynchronous orbit, you can deorbit them all one after another, perform the same deorbiting maneuver in the same way, and they will end up at the same location on the surface.

But I agree that from a career-mode point of view, this is kind of a constructed scenario. If you want to bring a lot of payload to one location on the surface, you would usually land it all together. If you bring multiple independent landers to a planet, you usually do that because you want to land them in different biomes, far away from each other.