In my opinion, the main problem with Trump's reliance on Twitter is not that he is going around the media; for instance the so called "establishment media." The problem is 140 characters or less. It's dealing with issues too complex for sound bytes. I know, he does, sometimes, split his messages over several tweets which could allow for more than 140 characters, but it's still kind of choppy.
Using social media isn't necessarily a bad thing for a president, or president elect to do. It doesn't matter that much what media he uses, Facebook, his own blog, web site or The White House web site once he gets in office. Whatever he uses, people will listen. They'll follow every word. The regular media will be right there also. Every utterance from a president, or about to be president gets reported on, discussed, analyzed, criticized, researched, and so forth. The media is there.
Problem is that the discussion needs to go beyond sound bytes. The media does flesh things out a bit this; or at least some of the media adds more depth. I find quite a bit of useful and deep discussion on NPR, for instance, just about every time there is a tweet from Donald Trump.
Another worry is who, among journalists, has access to the White House. Who gets to ask questions at press conferences. What information is being released and so forth. These are important questions and, in many ways, nothing new. I remember these issues around all the presidents.
The bad thing about reliance on Twitter is the lack of depth it implies which can go along with a lack of understanding. I find this problem, not just with things like Twitter, but with a lot of public discussion of issues, in general. Too many people don't have, or don't take, enough time to discuss and learn about things in depth.