I'm vegan, and on my honeymoon we went to a place where hens ran around free in the villages and would crawl underneath bushes to sleep for the night. Even I wouldn't see any ethical problems with humans grabbing unfertilized eggs they found under bushes each morning, but as I said, how many people would that feed?
It's the same as me having much less of a problem with hunting than I do factory farming, because a bullet and instant death, or at least within a couple of minutes, is a much better life for the animal than factory farming. But if we limited meat eating to only that being hunted, people would get to eat a small fraction of the meat they eat today.
Or rather, price would probably be so high that only the most well-off could afford the eggs and meat in that world. If you're in that group you might still get eggs and meat, otherwise not. Still, people who use these two examples as ethical ways of getting eggs and meat must also agree that we would need plant-based alternatives for almost all our current uses.
Also, as of 2013, 98% of hens in the US was in cages, and 2% free-range:
https://www.ciwf.org.uk/media/5235021/Statistics-Laying-hens...
In the EU, it was 60% cage, 25% barn, 12% free-range, and 3% organic. At least for Sweden, free-range can still be indoors, but organic requires access to the outside. So even moving only to current free-range eggs would mean a drastic reduction of consumption.