There is nothing preventing the power of their broadcast being trimmed back to fit their state of origin OR there is nothing preventing their having to apply to multiple states to have their broadcast in each state.
Regulating interstate commerce doesn’t mean owning it...no more with the radio waves than with the highways.
I don’t know. There was a time when large areas of the country had radio coverage from a few, out of state stations. If you lived in IA, for example, WLS in Chicago was pretty much the only show in town. Getting radio station signal patterns to match state borders can be pretty tricky as a technical matter. Plus, atmospheric conditions can skew the signals. Heavy sunspot activity, for example, can have a major impact on distance in the AM band. When the sun goes down, the distances increase dramatically, which is why most AM stations reduce power about 5X at night. I wish Common Tater was still with us, he was an expert on the industry. I was just an engineer.
It seems to me if ever there was a good purpose to have a federal agency to set the ground rules for an activity, broadcasting is it.