The only difference between a public intellectual and an entertainer or other content creator, is that the public intellectual had at least one novel idea about something important. I mean idea very broadly here, it can take the form of a reframing, an intuition pump, a system for reasoning, etc. That makes them known as "the guy who came up with x" vs. "the guy who makes videos about y". Rogan has a podcast, Taleb is the fat tails guy.
But even the best public intellectuals only have a few novel, high quality ideas a year. Most have only a few during their whole career. If someone only writes a book when they have something to say (a rarity for professional authors, more common amongst people who don't like writing). That book probably contains a few, maybe only one, novel idea. That's the case for books, what about tweets or videos?
Entertainers and public intellectuals compete for the same bandwidth. They show up in the same feeds. In order to compete, the intellectuals have to lower their standards, and the result is that many public intellectuals are only in the intellectual business 1/100 of the time, and in the hot takes business the other 99/100.