A ton of good. He is a rare positive and educational influence for much of the US male population that is being pulled in the other direction constantly. If anti-intellectualism is to be defeated he rather than any snobby academic is the best hope cause I feel he can get the concept that being smart is acknowledging what you don't know through to people.
I am a pretty anti free speech(as modernly interpreted which IMO is a license to be wrong more than a civil liberty) person, think the exchange of free ideas has been a pretext to muddy what a fact is, and has and will continue to have irreparable consequences. I just find the idea that the right idea will win the contest of idea's just on the merit to be laughable(climate change, trickle down etc). But Rogan's way of interviewing everyone I think is the best possible way that sort of thing can be done. His podcast is not all too different from say something on C-Span(say book tv) except the way he frames conversations means people will actually watch.
I think he might honestly end up being more influential in ending this era of predatory capitalism than someone like Bernie. Not cause he's smarter or has better ideas but just his ability to get people to listen.