An animal shouldn't be killed because it's too fat, no, but you do have to consider quality of life. It doesn't have to be functional as a wild animal, just functional and not in pain. If we're talking about a bird that's gotten to the point where its legs can't support its weight, where its bones break just from it living, where it can't move or do anything but continue to eat and continue to be in pain, the only humane thing to do is put it out of its misery.
We're not talking about disabled humans here. We're talking about animals. If an animal is to the point where it is no longer capable of doing things that it should reasonably find enjoyable, if it's in severe pain that can't be helped, and if its quality of life can otherwise be reasonably assumed to not be good, euthanasia should be strongly considered if not carried out. Sometimes, leaving an animal alive is a greater cruelty than killing it. That goes for terminally ill animals, it goes for animals that have been so severely injured that their recovery is unlikely and will be extremely painful, and it goes for animals which have such a severe genetic issue that they are going to be crushed under their own weight.
If you can keep your cornish X birds at a reasonable weight, if they still move without pain and aren't injuring themselves, then great. Keep them alive. If they aren't functional any more, or are rapidly heading that way, don't prolong it.
I don't think these birds should be kept in commercial situations, since the commercial places aren't going to afford them the courtesy of closely monitoring them and making sure they don't suffer- it's more profitable to get them to grow as fast as possible. I'm not really sure they should be kept as pets, either, or grown by the average farmer- they aren't going to live long even in the best circumstances. Sure, some people can keep them in an ethical manner, where they grow at a slightly more reasonable rate and don't suffer because of their own bodies, but most people won't bother.
