Something I've been grappling with lately is that everyone basically pretends to have an understanding of everything to some degree.
Most of our models of things are hopelessly low resolution cartoon versions of the real thing, yet we feel like because we know what something is, perhaps how to operate it, and perhaps where/how to acquire it then we feel like we can explain it in much greater detail than we actually can. This is the so-called Illusion of Explanatory Depth.
https://www.edge.org/response-detail/27117
I don't personally know if his models of Postmodernism and Marxism are ultra-low, low, medium, high or ultra-high resolution, but I would venture to say a well read University professor on the world stage talking about these Philosophies on a regular basis has at least read Derrida, Foucault, Marx and other primary sources. I'd be very surprised if he hadn't and if you could point to a an admission from him that would be appreciated.
For me, I came to learn about these ideas from him. His firebrand, sky-is-falling style of Rhetoric made it fun to listen to and ultimately I thought well I didn't understand it very well after listening to him for an hour, but I came away with a feeling it's important to dig deeper and do more investigation. I went away and got an alternative explanation of Postmodernism from Stephen Hicks who I thought explained it a lot better and clearer and I enjoyed watching that. I watched Thad Russell get into Postmodernism with Joe Rogan to hear it more from the Postmodernist side.
Ultimately a good professor sparks interest and debate and inspires people to get interested and learn. Peterson did that for me. I didn't necessarily take his version of things and just run with it but he made my ears prick up and he made me pay attention. I think that's really valuable.
Now the most legit criticism of Peterson is that whacky ancient snake paintings == DNA thing and he's justifying that belief purely just because he wants to and because an anthropologist got high on Ayahuasca, tripped balls and wrote a book. I'd expect more from an academic but hey... We're all human. Gotta take the good with the bad.