Because our voting systems are nearly all First Past The Post, voters are forced to vote strategically, based on who they think others are also likely to vote for (and their recursive assessment of those voters' assessments). In game theory, this is known as a Schelling focus[0], and it makes it difficult to reveal voters' true preferences for leaders and policies (as opposed to other systems like Ranked-Choice[1] or Approval).
This is often theorized as one reason for the effectiveness of broadcast advertising: in addition to individual influence, one becomes socially influenced by the awareness that millions of others have seen the same advertisement at the same time, and thus can be relied on to use brands and products as signals for identity or group membership.
So in this sense, even as the power of broadcast is waning in favor of social networking, broadcast media (such as televised debates) still have tremendous power in powerfully nudging the recursive algorithm: even if I know for a fact that a TV interviewer is cynically kneecapping Gabbard/Yang/whoever, the mere fact that I know so many others are seeing it will influence my assessment of their odds, and discourage me from "throwing my vote away", knowing other viewers are likely reaching the same conclusion.
Incidentally, as opposed as the MSM was to Trump during primaries, I think he still leveraged this phenomenon in his favor; partially by being so shocking that he gained regular airtime, thus seeming more prominent and significant, but most especially through his IRL rallies, which acted as a powerful signal of popularity, inline with the common knowledge model described in "Rational Ritual"[2].
[0] https://en.wikipedia.org/wiki/Focal_point_(game_theory)
[1] https://ballotpedia.org/Ranked-choice_voting_(RCV)
[2] https://press.princeton.edu/titles/9998.html