**I think** the prohibition stems from the 1930s when shortwave first got started. It more or less coincides with WLW being allowed to operate at 500kw and other major stations filing for a similar power increase. Network affiliations were important to radio in a way they'd be important to TV in another 25 years. Smaller local affiliates were afraid they'd lose their affiliations to a handful of monster stations.
Domestic shortwave would make the problem worse, making it easier for a handful of stations to cover the entire country.
I would think that local MW stations would become independents while SW stations are exclusively network programming, which is pretty much what is in demand in the broadcast industry today.
That's exactly what would have happened in the 1930s -- but since the most popular programming was on the networks, quite a few local stations would have gone bust.
Of course, today local stations have nothing to worry about, in terms of competition from shortwave. Receivers are rare (in relative terms) and the poor quality (compared to universally available local FM) leaves nobody really interested. (again in relative terms)
Why are the receivers still poor quality with the advances in technology?
Sorry, I meant the poor quality of the shortwave audio, resulting from propagation variations. The radios (and transmitters) are fine, but the ionosphere inserts distortion between the two.