At the same time, it is understandable for the President to be hesitant to allow such close access to their person, or to moments where things are said and done in a rather different manner than publicly presented. For example, if my girlfriend ever heard me say some things about her when I'm in beer-and-xbox mode with my closest buddies, I'd probably face a shitstorm.
Every once in a while when a politician forgets to turn off their mics and says something inappropriate, there's a kerfuffle about. But they need to be able to say those things in private. This pen-and-paper-only press-pool is a middle ground, so that the press can have some access, without having videos of inappropriate remarks or moments plastering across the 24/7 news media networks.
I see nothing wrong with this. Now on the other hand, if we are talking about the unusually cozy relationship of the media in restricting their criticism of the military, or military operations for fear of jeopardizing their embedded-access, then that's another story. Or the Washington bureaus cowardice in challenging the administration in the briefing room. I wish reporters would show more courage in those situations. But those situations are necessarily outside ones. They should gladly give up access, refuse to be cozied up to, refuse to go to those god-awful Correspondents' Dinners where they are wined and dined and bought. That I would heartily support.