I listened to the podcast, which as it says focuses in particular on John Mew and son, John apparently being on the cruel and crank end by experimenting on his children including on his daughter with expected negative results, and his son now reportedly showing a flair for bringing pseudosciency selective evidence to promotion on social media, and more recently perhaps helping "incels" fix "weak chins." (AKA, perhaps a focus for unstated outrage to help motivate a slightly-weak podcast)

I was offered a tongue depressor by my childhood dentist to help fix a crooked tooth without orthodontia, so when Nestor's book mentioned one orthodontist suggesting that positioning one's tongue to touch the roof of the mouth would matter, I dismissed that part as probably the weakest in the book. That said, the science overall seems to be evolving, research in breathing and the nose apparently increasing, and Nestor is meticulous in maintaining references, including online. Many might be comfortable with some uncertainty and not dismissing this all as pseudoscience. I commend Nestor's reporting.

I also hope that, if industrial civilization eventually passes, and for now where severe poverty without dentistry exists, people will find again whatever practices better prevented dental caries.

I was born with a deviated septum and for the first 15 years of my life I just assumed breathing through one’s mouth was normal and the nose was just for smelling things. After surgery I started breathing through my nose without conscious thought for the first time.

Yes, certainly for heavy congestion. However, for marginal cases, there might be some body adaptation made to help with efforts at nose breathing. .. Nestor avoids giving specific recommendations, given individual variations and needs. But the research seems to point to: there is a lot going on. For example, apparently the nose contains erectile tissue, perhaps helping explain how one can cycle between now one nostril being easier to breathe through, later the other. .. My very limited experience, living where I would usually call myself "always congested," is that given a little effort/intent at nose breathing, I now sense that my congestion is consistently less than before. (But N<1 as evidence, since there could be some seasonal change as well.)

Or extracts from sweet fruit like this:

https://en.wikipedia.org/wiki/Powidl