There are plenty of locales where broadcasts cross state lines. I grew up in an area where we got Boston (Massachusetts) and Providence (Rhode Island) stations. NYC stations cover three states. I'm sure there are plenty of other examples (probably involving even more than three states).

So the justification for federal intervention (interstate commerce) is there.

Of course, that doesn't prevent the feds from letting the states handle it, but it does create an incentive for some states to want the feds to handle it.