> I'm not sure one rocket can launch a geostationary satellite above the Americas and above Europe in the same mission.
Easily. Moving within an orbit is a matter of fine adjustment. For example, any stationkeeping that expands the orbit slightly will cause the satellite to "fall back" over time. Geostationary satellites are the best orbit for this, since every satellite in such an orbit essentially shares it with all others, differing only in position along the orbit.
I'm not sure this is true. if it were, there wouldn't be launch windows because any correction within a given orbit would be, as you call it, "a fine adjustment" yet we clearly do have launch windows.
Also if you're in a geostationary orbit to deliver one payload you have to leave that orbit to get to another geostationary orbit because there are other satellites in your way.
It is a fine positioning, which takes time. The launch windows get you to the right spot right away. Someone paying for a dedicated launch doesn't necessarily want to wait around to get their satellite operational. Someone launching for cheap on a rideshare might be willing to.
Easily. Moving within an orbit is a matter of fine adjustment. For example, any stationkeeping that expands the orbit slightly will cause the satellite to "fall back" over time. Geostationary satellites are the best orbit for this, since every satellite in such an orbit essentially shares it with all others, differing only in position along the orbit.