Unless you sincerely think there's going to be widespread political violence in your specific area, knowing about what's going on in at this exact moment is honestly as much about entertainment as anything else. And if you need local news, the NYT is typically not the best place.
I'm as guilty of rubbernecking as anyone, but I wouldn't go so far as to claim that boycotting my favorite news source for a few days would be extremely damaging to me.