This really sucks if you are homeless and don't have a refrigerator. Another great source of protein unavailable. (as once it's washed, you can't safely keep them at room temp anymore).
If you are homeless but living in a vehicle and have some means to cook, there are ways around such issues. For example, you can store cold items in a cooler, no refrigerator required.
When I was homeless and sleeping in a tent, we sometimes kept perishables for short periods by leaving them outside the tent overnight in cold weather or keeping them in the backpack and keeping it out of the sun. If careful, butter sometimes stayed semi solid for a few days.
Modern refrigeration is not the only possible solution. It's just the most familiar for most Americans.
Plus, a high percentage of homeless Americans have serious health issues. If you are, for example, being treated for cancer, you aren't supposed to eat, for example, raw cookie dough because of the raw egg it contains.
With that being said, I believe American eggs can still be safely kept at room temperature up to several weeks.
Yes you can. I'm in the US and I've been keeping my eggs on the counter for years now. They last for months and I have not had a single spoiled one except if it was cracked.