> Sensationalized TV coverage of mass shootings may encourage more of them

Sensationalism sells ads. You're asking the media to act against their own interest in order to serve a greater public interest. But if one outlet doesn't do this, another will. Therefore such coverage is inevitable with a competitive free press.

A non regulatory solution would involve making such coverage not sell more ads. That means making sensationalized murders less attractive to viewers. That means reshaping human character in a fundamental way. Quite a project.