The real question you have to ask here is if the shortwave spectrum didn't have some form of broadcasting, what else would we do with it?
Shortwave as a long haul communications medium has largely been left behind as satellite radio became more popular. However, I think that shortwave broadcasting might improve in several ways:
First, I know the romance of AM is certainly there; but, honestly, it's got to go. Even Double Sideband Suppressed carrier would be better. But that said, I think a modern digital modulation method that is resilient in the face of selective fading would be best. That's what DRM was supposed to do, but then they ran in to issues trying to build affordable radios for this mode. It still hasn't taken root the way everyone had hoped.
With software defined radios for SW dropping in price the way they are, though, I have to wonder how long it will be before SW broadcasting with complex signal demodulation gets popular again. Another point is that data broadcasts are getting more and more useful. Radio stations might be able to broadcast schedules that your receiver could automatically pick through to find the signals.
I think the shortwave spectrum has potential. It probably won't be for music programming; but I do envision a broadcast service that might be useful for weather, rural information (such as visiting medical teams, farming and climate forecasts, road conditions, and the like), news, and so on...