I think the general argument that the media is not effectively using the attention these events draw is in direct conflict with the idea that these shootings are "predominantly media hype".

Also, I quite frankly think this mindset is naive to how both politics and the media work. Nothing materially is being done to reduce school shootings and today's tragedy is just another example of that. So why the fear that this need for a solution to general gun violence will be satiate by a solution to school shootings? We aren't getting any solution to school shootings either. Plus most of the mainstream media has a desire for neutrality that would prevent them from doing what you suggest. And those that aren't opposed to being seen as partisan and agree with you about overall gun violence are already advocating for greater gun control in a way that is not exclusively set to address school shootings.