That's not really true. The thing which is a natural monopoly is the last mile, which is inherently local. You could literally have the city government own the fiber and lease it to competing private companies without any federal involvement whatsoever.
The main impediment to this is that the incumbents are too large, which allows them to overpower city governments in terms of lobbying and prevent anything like that from happening on a widespread basis. But if you had some hypothetical state government with the will to stand up to them, that would be the end of it.