Veganism is about being pragmatic. It's not a dogmatic mindset. The main goal is to not harm another sentient being. Both factory farmed or 'happy' farmed animals usually end up in the same slaughterhouse. Pigs are being gassed and have a terrible death. And in general, animals feel when they are about to die and then start to panic. In the words of Carl Sagan 'they are too much like us'.
Look up Mike Bisping, someone you would typically class as a tough man. Even he couldn't work in a slaughter house. So imagine what it does to your psyche day in and day out having to kill animals. Slaughterhouse workers suffer from PTSD. In one report one worker described how a pig came up to him and gently headbutted him (like a cat showing affection). He had to suppress his compassion to be able to kill it. How effed up is that?
We can vote with our wallet to reduce or stop all that.
In regards to eggs, I would say eating eggs from chickens you have in your garden is OK. There are folks who rescue chickens and let the roam in their garden and eat their eggs. There are certain vegans who complain about that. That is being dogmatic.
And what you suggested, eating meat from animals who died naturally and didn't have to be killed for you, I'd even class that as vegan, because no animal had to suffer. But it wouldn't be profitable as a business, so I don't see how it can work on a large scale or replace factory farming.
We need cultured meat or simply train ourselves to enjoy plant based foods. Dr Wareham said it will take a few weeks for your taste buds to 'like' other foods. And you get enough of nutrients and protein from those foods. Plenty of top athletes prove that point.
Or folks who eat road kill, I'd say that's also vegan. The animal died by accident. You didn't pay for it to be killed, i.e. you didn't contribute to the demand that keeps the meat & dairy industry running.
EDIT: typos & clarity.