The important thing for getting bureaucracies to do what you want is to make it expensive for the bureaucrat to not deal deal with your problem. That's a distinct advantage to calling in - you're using one of their employees time, and you will continue to do so until you're satisfied. The line agent wants to handle you ASAP for their statistics, and if you get escalated then even better.

Tweets are just an extension of this. It's immediate negative public PR, and there's people whose job it is to manage it. You get an outsized amount of leverage in the "how will my issues get solved" negotiation.