Problem:
"...the FAA does not have any power over launches that happen outside of the US. As with many of the problems in space, the world currently lacks an international approach to space debris"
That's not a simple matter. Currently, there are national authorities and organizations that regulate every aircraft, even balloons - schools must theoretically have an authorization before launching those balloons with a portcard. They do that based on the ICAO recommendations, at least for the nations who signed up. It's a little fuzzier above international waters, but it's usually the responsibility of the country where the aircraft is registered (*), with some regions having their own organizations.
As for the altitude limit, I had to look it up. Countries usually agree that altitudes above the Kármán line (100 km) is not in the aviation playground, and leave everything beyond to
chance the space agencies. It makes sense, since this line is in the thermosphere,
where normal civil aircraft would feel uncomfortable if they could get up there (they can't).
But now, it seems to get more complicated with private companies dropping things above our heads. Maybe it will follow the same pattern as aviation had with the Chicago Convention and ICAO?
(*) So if SpaceX's rockets are registered in the US, the FAA should have its say in the matter of the launches, but I suspect it's more complicated for the satellites dropped by those rockets.