To be considered as influential, a blog in some way inspires their readers to be more productive than just doing simple reading and commenting.
A single post from one of these blogs starts off a long conversation that incites other blogs to join in, drama or otherwise.
Or their blogging style/personality inspires people to try their hand at blogging themselves.
As such, The blog often is given the role of a tutor, giving explicit and implicit advice on various aspects of anime blogging from how they do things.
These are blogs that when they move, the community moves with them, for better or worse.