There is one thing that might be worth docking the SE for: You could use the SE to launch very large spacecraft from GEO to higher orbits, including moon, Mars, and other solar orbits. Even though the SE may only be capable of lifting 20 tons from the ground, you could attach a much larger mass at GEO and let it slide outwards, unpowered and unbraked, until any desired velocity is obtained.
So build spacecraft in a dry dock near GEO.
Tow it to the SE.
Fuel the spacecraft and put the people & cargo on board.
Launch by sliding up the ribbon. A smaller climber will be needed at the start of the slide.
The ribbon has low rather than zero friction, so a method of cooling the ribbon and slider may be needed.
Release at the correct time and the correct height.
Fly to the Moon.
Fly back to ribbon and unload the people & return cargo at GEO.
Send the people down to Earth.
Inspect the spacecraft and scrap if warn out.
Repair, refuel and put more people and cargo on board.
Launch again.
Fly to destination
Return.
Repeat.