To temper expectations a bit - last month another private company attempted the same and had a problem in-flight, eventually leading to basically a failure of mission.
Hopefully IM-1 doesn't run into any issues, but landing on the moon is hard. I think of the last 10 or so moon landers, only ~50% actually successfully landed. Most recently Japan managed to accidentally land upside down!
So best of luck to IM-1, but don't count your chickens yet.
I have wondered if SpaceX has been interested in pursuing launching from the former Soyuz pad in French Guyana. They've saved Europe's bacon by picking up their stranded payloads, one would hope that would make them amenable.
All the infrastructure is there for Falcon. And the fact that it is so close to the equator means they should be able to do more rtls launches.
Probably mostly legal rather than technical issues. Barging rockets down there would be an added expense over those of transiting to US based launch sites but if launches end up at a frequency that launch pad availability in the US becomes a bottleneck, doubt the additional cost would be much of an issue. And as you pointed out, for certain missions the added boost of an equatorial launch would be ideal.
Iirc Elon mentioned something about SpaceX being legally restricted from operating outside the US. Obviously there are national security implications, given how they're working on the most powerful rockets on the planet. My guess is it would unlikely be approved. Most of all they probably want the scientists and engineers in their own jurisdiction.
There is precedent. Rocket Lab is technically an American company yet launches out of New Zealand.
If SpaceX was selling a rocket to the EU or letting the Europeans operate the rocket a license might be difficult. But if it was only SpaceX personnel who had access to the rocket? I imagine a license would be likely. Not guaranteed, but likely.
I think it opens them up to a lot of political risk. Outside just the logistics of figuring out how to export the rockets, French Guyana is not the most stable place to launch rockets from... And from what I've seen at Elon I don't think he'd be any better at reducing tensions than the ESA
Their logistics advances to make this possible are very impressive. Still, I think achieving their stated goal of 12 launches per month will be very difficult to achieve with the number of pads they have. Weather, range contention, payload delays, barge issues, etc can all cause bottlenecks.
Example, a little while back there was delay in a FH launch. This rippled down the schedule because it takes time to convert the pad back to F9 mode.
IM-1 has also been successfully deployed. We'll likely see the first private "soft" moon landing in history and the first from the US in decades.
https://de.wikipedia.org/wiki/IM-1