Agreed. They will mate freely and lay freely. They really don't care what the other breeds around them are.
The dual purpose breeds were developed for what you seem to want. They lay pretty well and eventually get big enough to provide meat.
One big difference in eating dual purpose chickens and Cornish X is that the Cornish X are big enough to eat at a very young age, normally 6 to 8 weeks. For dual purpose breeds they will have to be a lot older to provide much meat. I don't even consider eating mine until they are at least 15 weeks old and really prefer them to be older. What that difference in age means more than anything else is that you cannot cook them the same and get the same results. Many people think that the Cornish X are bred to provide tender meat. I don't agree. I think if you process a 7 week old dual purpose bird and cook it, the texture and taste would be the same, you'd just have to look a lot harder to find any meat.
I don't even consider frying mine. I braise, roast, stew, or most often, use a crock pot. It takes a longer, slower, moister method of cooking to really get them to do well in the kitchen.
That brings up another point. Many of the recipes you get in recent cookbooks or online assume you are getting one of those really young birds from the store, not an older dual purpose bird. Even if you braise, roast, or stew it like they say, an older bird just will not cook right. You need longer, slower, moister cooking methods for them to get really tender. I think that's why many people get turned off our home raised chicken.