It's a wonder the Cardinal survives without people putting out bird feeders....Seriously? The jungle fowl and up to modern chickens can forage quite well. If left alone would naturally select back to great foragers, hearty to whatever climate they happen to be in and go broody each spring at the very least. More over would survive with varying patterns that would weed out white birds for camouflage.
You are right. If they were left in the wild, the broody hens would be the only ones to reproduce, and also the ones that can forage and fly high enough into a tree to avoid predators. But because they are domesticated there are breeds that can't fly or won't go broody, and those traits would not work in the wild. But people want chickens that can lay many eggs and/or have big bodies for meat. And some are bred by people for pretty feathers.
Cardinals are one of the few birds in the colder regions of North America that don't fly south in the winter because they can find enough food through the winter. I am sure bird feeders make it much easier for Cardinals to survive through the winter, but Cardinals were surviving through the winter long before people put out bird feed. There are always Christmas cards that depict Cardinals in the snow. The Cardinal is often on a holly bush or something, so that there are the red and green colors of Christmas, which come from a holly bush with its green leaves and red berries.