People try. Most are disappointed but a few are successful. The most successful tend to be the ones that keep females and cross them with dual purpose roosters. Check out Compost King's thread below in this section about crossing red rangers. That's a long thread but some really good information in it from several of the posters.
You'll need to keep the bird on a strict diet to avoid the overeating; it's in their genetics to overeat and get big fast. Problem arises when they grow that fast is that their bones don't have time to catch up to their weight gain, and can easily break under their own girth. I agree that they have the sweetest disposition. I had one years ago that I named Bertha, she lived well past her life expectancy and was an absolute sweetheart.
I tried this spring with one Cornish X broiler, it died around week 15 when the temperature reached the high 90's. I am trying again now with Birds that hatched at the end of July. I have 3 of them (bought 6 and 3 turned out to be males and I am ate or will eat them) The one that died kept her weight down and was running and even flying short distances to get over obstructions. However she couldn't handle the heat. I am hoping to keep just one of them long enough to breed then cross her with my Naked Neck or my free ranging broilers. If all 3 survive to point of lay then I have more breeding options.
I just go back from feeding my Cornish X pullets that I intend to breed. People say to use a lower protein feed but the only lower protein feeds I can find have a high amount of Calcium. Mine are not laying yet and high calcium can be hard on their Organs. There is always Dumors 'Grower finisher" which is a 15% protein feed but I have had issues with Dumor to where I won't feed it to my chickens. I just went with 20% (high) protein meat bird feed and gave them less of it. they have a compost pile to dig through for more feed if they are so hungry and they do dig through it a bit but not all day. Usually when I look over at their pen they are sitting at the fences closest to where I tend be when I am outside waiting for me to arrive with feed. I feed them through out the day sometimes 3 times a day sometimes just once, depending on how big they are and each feeding is a little over once cup (there are 3 broilers and 3 buddy birds that show them how to forage)
The Buddy Bird program! When I ration feed to CX females to breed them I keep then with what I call Buddy Birds. Heritage breeds (or crosses) that will forage when food is short. The CX girls start to mimic them. I just use what ever I hatched at the time but if I planned things out better I would use Leghorns as Buddy birds because they are prolific foragers. I am the only person I know who does this but its such a simple idea that I am certain that others do it too.
I know I am late to the discussion, but there's a farm near me that has broiler breeders - thousands of Cornish Crosses, both hens and roosters (one of the industrial strains, not sure which), and they have no trouble getting these birds to reproduce. They lay very large off white to cream colored eggs. They keep them for a year, then "recycle" them. So, it can be done. These birds have their feed tightly regulated, which as I understand it, is required to get them to adulthood. From my research, they are free fed for the first 5 days, then get food with held for 12 hours a day, to slow growth.
Not sure what mortality is after a year though. They all become soup meat. But they are early and fairly prolific layers, laying from 20-26 weeks, and each house of 10,000 chickens (no idea hen/rooster ratio) produces 6-8,000 eggs a day, which is a daily or every other day layer. This farm is specifically a farm for hatching eggs to make little broiler babies.
I'm pretty certain that Cornish Cross Broilers are a 3rd generation cross breed. If you are able to successfully breed them, you won't necessarily get Cornish Cross chicks. I've heard of a few that tried but, I don't think it's very economical to do it.