NASA’s charter is development and exploration… making them a regulatory agency just wouldn’t work.
We need correlation for use of airspace, and we need some sort of regulatory authority that can monitor and regulate the dangers to the populace. In China, for instance, the major launch sites are well inland and they regularly drop burned-out stages into the countryside.
Some argue that such “regulation” should be handled by liability laws…if someone thinks they’re damaged by a piece of space hardware, they should be able to get “whole” by suing the company. The trouble is here, that Elon Musk has much, MUCH more money and lawyers than a farmer in North Dakota with a hydrazine-contaminated pasture.
So I think we need some sort of regulatory agency. Dropping this in the FAA’s lap makes about the same sense as making Space Force a part of the Air Force and controlled by it. I think we need a dedicated agency specifically tasked to regulating US space operations, and our primary interface with the international community.