Because in signing the 1967 Outer Space Treaty, it accepted responsibility for all launches emanating from the United States. It has to regulate the activity in order to maintain that responsibility. And even in the absence of that treaty, public safety dictates that it be regulated. That's like asking what right the government has to regulate aircraft.
Huh? How is a satellite launch a threat to public safety?
That's like asking what right the government has to regulate aircraft.
What right does the government have to regulate aircraft?