I also suspect his topics just appeal to young men (fitness, comedians, Elon Musk) and that accounts for a portion of his base.
Embracing ambiguity is fine when there is genuine ambiguity. Portraying minority or fringe ideas as 'ambiguity' is dangerous.
The problem with what you're saying is that you're setting yourself up as an arbiter of reason, or sanity, or safety in the realm of ideas. This is a fine aspiration, but you can clearly see that not all, or even many, will accept your analysis.
So you go into problem solving mode - and end up with government, or trust and safety boards, or religion, or any of the myriad of communities humans develop to corral the marketplace of ideas.
All of those systems suffer from humanity's profound fallibility and until that stops being the case, actually talking out all issues will be the only reasonable method of handling freedom of speech.
Some limits are obvious, but because human fallibility is so profound, we should be equally as profound in allowing ambiguous ideas the space to be understood and charity in interpretation. To do otherwise is embracing ignorance and folly.
The challenge of competing worldviews is really one of the central sociological challenges today. The natural tendency seems to be to try to push the contaminating thoughts to the margins of society - and all groups (left, right, religious, secular, etc) engage in this basic tendency. Its disturbing to live with people who's basic view of reality challenges your own.
The NYT represents mainstream left's attempt maintain worldview solidarity (and again, each group engages in this activity) so it seems natural they take issue with Joe Rogan as he represents the other choice in responding to the smorgasbord of modernity: engage with all the alternatives openly. Rogan states several times the format of his podcast is designed for this - 4 hour conversations. Not scripted, not planned, just conversation. Such conversations are apparently deeply interesting to people who'd rather not spend their time in parochial attempts to shore up their own worldview across society.
I do find it hard to tell (sometimes) whether Rogan's guests are on the level, but maybe that reflects the inherent ambiguity of life. I mean relativity in epistemology, ethics, and aesthetics has been mainstream for decades, if not generations. I expect the attempt to turn back the clock on modernity from conservative religious groups, but its always seems strangely inconsistent when coming from the NYT.