> Where/how did we fail in our educational and cultural activities
The glorification of "contrarianism" is probably a good place to start. Nobody trusts institutions any more. Nobody trusts experts any more. However, they do trust people they see as their "rebel" kin, whether that's Paul Krugman or Alex Jones. That creates an environment ripe not only for political disinformation but also many kinds of profit-oriented manipulation (e.g. yesterday's bust of YouTube pump-and-dumpers). Contrarianism is not the same as true independent thought; more often than not it's just delegating one's thought processes to different people.
This infatuation with contrarianism itself has a complicated history. The current strain tends to be right/libertarian, going back approximately to the Reagan era. But before that the hippies were strongly anti-establishment in their own way. (If you want to see how this kind of left/right shift works BTW, you could do worse than to study the life of Lyndon LaRouche.) From a longer view, this same set of attitudes goes back at least to the founding of the US, with a vision of liberty that was heavy on individual freedom of action but light on things like responsibility or collaboration. The actual Enlightenment philosophers in Europe mostly had a more balanced set of views. Many people who love to cite Adam Smith, for example, are shocked when they see what he actually had to say about these things. Somehow, though, only half of the Enlightenment message made it across the Atlantic. (Quite likely something to do with the religious element, but that's a whole essay unto itself.)
Back to the topic, Musk is very much one of those "anti-establishment" influencers, but becoming establishment himself which is why so many former fans are now turning on him - joining those who had enough historical/philosophical context to see already what kind of person he is. You need look no further than any Musk/Tesla/Twitter story right here to see this happening.
The problem is not so much that institutions don't exist but that they can't exist in an environment where nobody trusts (and therefore supports) them. First we need to draw a clearer line between contrarianism for social capital vs. actual independent thought. Only then can people see which now-dismissed institutions actually support and/or embody such thought, and begin to trust them again. Until then it will just be one cult of personality after another.