Trump only checks messages on twitter. He says that he doesn’t do email.
x% of the messages being sent to Trump on twitter are just cheering, 100-x% are hate messages, and approximately 0% contain critical, need-to-know information. Considering the volume of tweets he gets, I would assume that all his staff has time to do is scan them for the general flavor (i.e., the value of x from day to day). Any tweet that claims to contain critical, need-to-know information will be drowned out by thousands of noise messages and, even if seen, may take hours to vet. It is not likely that they will have the time to chase all of them down as possible leads to something useful.
When I first got my twitter account, I immediately set up "follows" for several of my favorite talk show hosts and commentators. After a couple of days of receiving hundreds of noise tweets, I unfollowed them all. I would take ranting tweets from the general public even less seriously.
I just logged onto my twitter account and checked the messages being sent to Trump. One every couple of seconds, 100% noise.