Because Travel Mode is an indicator that you've got something to hide, and thus, must be using social media to send encoded terrorist messages.
Maybe, but most likely they'll just see you as another nuisance maker trying to make their job difficult. And in their opinion it's important, valuable, patriotic and you're either non-American or one of the wusses they defend. I'm sure the TSA system has some informal way to shitlist a person so he'll get picked for extra security screenings, luggage checks, extended questioning, "problems" processing forms etc. so any kind of solution that lets the TSA know you're trying to obstruct or evade them is kinda a non-starter.
Sometimes I think terrorists are just nature's way of weeding out the violent and stupid- especially suicide bombers.
I think we'd run of places to blow up before we'd run out of violent and stupid people. Also, most of them manage a pretty solid kill:death ratio so if 50 people of average intelligence dies and one nutjob the average doesn't move much at all.