I think that's a key point both for chickens and other animals. It could be that static postures and processed food may not go well together, like they don't for humans.Exercise is surely a part of all this
The way food is given out has an impact. Encouraging movement like @centrarchid.
I know it's beginning to be taken into account for horses with things like horse tracks and paddock pastures.
They also take much less time and energy for their owners to prepare. While I would like to feed my chickens like you, I haven't found a reliable source of protein sufficiently near (less than 2h30 drive away) or online. Peas or organic soy just aren't sold in 10 kilos bags here. I would love to barf the cats but we are 90% vegetarian and I would have to get a second freezer to do it. (They do half barf themselves eating out rodents and birds though.)Animal feed concentrates (aka pellets, kibble, whatever it is that lets an animal - dog, cat, horse, cow, pig, chicken - get its day's requirements in much less time and with much less energy expended than it would if they were finding their food themselves) are upfs.
I wasn't aware obesity in domestic animals was such a problem. I can't help wonder it doesn't have as much to do with being sedentary/ confined as with the quality and quantity of food ingested. Health is a holistic thing.