Yeah, once you have a large ship out of earths gravity well, would be a waste to land it back on earth. Heck, even if it breaks, park it in a stable orbit so the next generation can salvage it for parts as needed.

PSA: Most orbits around Moon are not long term stable due to underground mass concentrations.

Neat! If you park a satellite at moon geosychronous orbit how unstable is it? Would it be lost in the order of months or decades?

Does that also effect the Lagrange points for the moon? Do human currently have anything parked at earth moon lagrange points?

There appears to be no such thing.

"the radius for a selenostationary orbit is much farther than the Hill radius, meaning that no stable orbit can be achieved as it would be too much perturbed by the Earth and/or the Sun"

"all of the Lagrangian points of the Earth-Moon system are stationary relative to the Moon surface"

...but then it is explained that stationary doesn't mean stable.

Links: https://astronomy.stackexchange.com/questions/20499/is-it-po...

https://en.wikipedia.org/wiki/Hill_sphere

The Lunar Starship has enough dV to land on the moon and return to orbit, about 3.44 km/s but boosting from the moon to Earth and braking into Low Earth Orbit actually takes more dV than that, about 3.94 km/s. Unless they build in extra 0.5 km/s capacity or about an extra 20%, it flat out won't be able to do it.

Here's where I got the idea and some different calculations: https://caseyhandmer.wordpress.com/2021/03/26/lunar-starship...

The diagrams say "Crew transfer in LEO or direct entry of Starship" as if they're interchangeable options, but these are not equivalent. Returning from the Moon and braking into LEO takes just as much dV as transferring from LEO up to Lunar orbit. Per the diagram that's 3.94 km/s as I said.

Conversely landing on the moon and returning to Lunar orbit takes 1.72 km/s twice, which is again consistent with my numbers if we assume the payload mass is constant. That may not be the case of course but any cargo taken from the Lunar surface to Lunar orbit will also need to be brought back to Earth somehow.

It would need lunar or high elliptic refueling to do that. Which is possible, but more complicated.