Free speech protections are meant to protect the citizen from government over reach. Squabbles on campus don't rise to that level.

The examples given are not about a free exchange of ideas. It is when colleges give an unchallenged megaphone to controversial speech.
Students protesting that are exercising their own speech. In this case silencing the students by government action is a violation of free speech.

The solutions to kids shouting down guest speakers are the same as at rock concerts. Good organization and security. Unfortunately that would cost money that the sponsors of controversial speakers are unwilling to pay. They also loose the notoriety and resulatant publicity they get for free.

The media feeds on chaos and controversy they need it so much that they are more than willing to manufacture it themselves. The Washington Post is one of the great malefactors in this regard.

But more topically the media are among the greatest clamps on the exercise of speech. So it is no surprise that they point the finger at powerless students rather than at themselves.