About the nutrient loss, I think that would depend on the means of transport and storage.
A few thousand years worth of chicken domestication is a lot because in chickens, a generation is about 1 year from what I understand about chicken biology (which isn't much). Maybe it's more than 1 year, but it's certainly much less than the 16-20 years we think of for humans. Going through more generations means the DNA has more chances to adapt to a changing environment. And with domesticated animals, the smart human breeder can provide an additional selection pressure, looking for health in the animal as well as healthgiving properties of their meat and products (eggs, milk) when consumed by us humans. Even if you disregard the artificial selective pressure (breeding), 2500 years worth of chicken domestication would be around 2500 generations from my calculations, which would be the equivalent of how humans have been living for the past 40-50 thousand years. Still not that much when compared to 500k to 2.5 million years of proto-human evolution, but it's something. Archeologists believe the humans species in it's modern recognizable form has only existed for 100k to 200 thousand years. Chances are there's been changes to the DNA pool along the way also, just not so intense that they would be able to easily tell from fossils.
About AV and eggs, iirc he said that they're wonderful for healing, just not for rebuilding. Which is kind of weird because chicks grow on eggs and they don't need to heal much, just build. Many bodybuilders use toxic egg white protein extract as well as whey protein extract from milk to increase their muscle growth. And even though the proteins have been processed and dried, it works. I would tend to think the way it would work in nature would be the opposite. That eggs and milk would be better for building, and meat better for healing. (the way people used to place a steak on a bruise instead of ice). If I think about it, a carnivore is likely to get minor injuries while hunting. Then the meat would supply the perfect nutrients for healing. Maybe what Aajonus meant was that eggs are good for pulling and binding to toxins.
I've never had wild meat other than fish, so I can't comment on the taste. I'm sure they taste better. I would love to try some. However, we need to realize that while it might be the best for our health, it's not applicable on a mass scale. Which doesn't mean some of us can't enjoy the benefits, but we can't expect everybody to. According to calculations I've seen, the average fertile and wild land only naturally provides enough edible food for around 1 person per square mile.