* meat: my family is from a village near Rome, Roman traditional cuisine is famously full of recipes that use all sorts of weird meat cuts (pork jowl, internal organs of various animals...) - you won't find most of those in an average supermarket. When it comes to meat, the problem is not just cuts, but also breeds: I live in Australia and it has been extremely hard to find chicken which is not Cornish Cross. In Sydney, you can find heirloom breeds chicken at only a handful of speciality butchers, and prices are very high.
* grains: this is a well known problem, most grain-based products are based on just a handful of varietals. I have to say that the situation is starting to improve: recently, in some upmarket stores, it has become possible again to get products based on some heirloom grains, however they are pricey (example: Pasta Monongrano made from Matt or Kamut flour)
* fish: it is a known problem that fishing boats are forced to throw away certain catch, because certain fish varieties are not "marketable"
the list could continue...
There's probably still an effect in there, but it seems more likely that it's mainly antibiotics that are killing off gut microbiota variety, with an argument to be made for a role of highly processed foods.