Blocking only NYT might not change things significantly, but showing that they will ban anyone who asks difficult questions means the ones who are left will think twice. The ones who keep "misbehaving" will also get banned. That will change things for everyone trying to get news.
The banned parties should make an alternative venue that asks questions of shadow governments. It will be more interesting and erode the Presidents power to choose how to address the people by overshadowing his useless PR and making the other governments easier to imagine.
Also fun, but I didn't mean a cutout of trump.. an actual clinton or sanders, or anyone who has some backing to run next term can build a shadow cabinet and start answering the NYTs questions.