I don't see the connection.. the only reason an airport would have to
ban a freelance CFI would be if they somehow miss out on a cut that
they otherwise get from an FBO employed CFI. Of course there could be
liability or even security reasons although they don't make much sense
to me either.

The airport has to have a functional FBO, at the very least to sell
fuel. If there isn't one, keeping an airplane at that airport is MUCH
harder, and there will be fewer airplanes there. With fewer airplanes
there's less reason to have an airport, and more reason for the city
to sell it off to a developer.

Most FBO's are struggling to get by. The FBO earns some part of it's
income from flying lessons - so theres a reason for the airport to
support the monopoly FBO.

Some airports have tried to ban free lance A&Ps. There's usually an
excuse, like safety, but it's really the same reason.