Trump dumping the Eagles brings together two things that his supporters like about him.
1. He fights culture wars
2. He doesn't care about the liberal consensus, but the conservative one.
Past Republican presidents would occasionally, very tentatively, wade into culture wars, usually with a nice speech, that would be roundly mocked. And then retreat. Think about Bush I's critiques of popular culture.
Trump's culture war setpiece isn't the speech, but the tweet, the off--the-cuff remark and the action. And it's effective. He forces the left to defend something that most of the country dislikes, whether it's the anthem protests or Bee's vulgar insult.
Conservatives who agree with him often complain that he overdoes it. The point has already been made. He didn't have to call for firing Bee or boycott the Eagles. But they miss the point.
And that's point 2.
Establishment Republicans tended to address the liberal consensus. That was inevitable because if you spend enough time in D.C. and dealing with the media, that's where your narrative comes from.
Trump spends a lot of time dealing with the media. But he addresses a conservative consensus. And that's a key point.
Too many Republicans only address the conservative consensus on the campaign trail or when asking for cash. Trump treats politics as a team sport. And he understands that you need to score and you need your home crowd cheering you on. That's a point that plenty of Republicans in D.C. forget. So he fights culture wars because it's dynamic, effective and mobilizes the base.
He doesn't give setpiece speeches about it. instead he tweets insults and takes action. That changes the conversation and forces the media to defend the next terrible lefty cause.