Mutt chickens are extremely common. We all have different goals and reasons for keeping chickens. I cannot speak for anyone else, but I personally chose diferent breeds that should give me decent dual purpose chickens when they interbreed and, after a couple of generations, I will never know what the chick will look like as long as I don't overselect for one color or pattern.
I've seen it suggested that if you keep interbreeding mutts, they will eventually lose fertility, egg production, growth, or some other positive trait. That's why you keep purebred chickens. I think if you keep interbreeding from the same purebred flock, you will run into the same problems. Eventually you will need to bring in some outside blood, whether that is from another purebreed strain or just another mutt flock in my case.
I'd guess one reason you see a lot of purebred chickens on here is that a lot of people are showing you their first generation of chickens. Also, many do not raise their own replacements but buy them from a hatchery. In either case, hatcheries normally sell either purebred chickens or special crosses like the sex links.