>>>Personally, I think a private agency would do a much better job.
I disagree. Private companies can not negotiate treaties with other governments regarding interference of RF signals... that’s one of the things the FCC does under authority of the enumerated powers of the commerce clause, and the Senate’s duties in regard to treaties.
This is why government never shrinks. No matter how blatant the over-reach, it gores somebodies ox.
BTW... If you want a preview of what a PRIVATE run FCC would look like, look up the IEEE or Underwriters Laboratories.