Yes, the media were and are in a similar position of power, and despite some bumps in the road they've turned out to be a very good thing.

I don't object to a good-faith defense of Twitter etc. as arbiters of truth, because it's entirely possible they'll do a good job and become a responsible authority. I do object to the idea that only the political right would have a problem with them, and that the only problem anyone could have is tyranny of the majority. I'm more worried about tyranny of Jack Dorsey than tyranny of the majority.