That's close to what I try to do, but since I raise chickens for meat as well as eggs and I will never get all the broodies I need for that, I went ahead and got an incubator. I intend to raise my own replacement layers and roosters as well as lots of extras for meat. You can keep doing that but eventually you will lose so much genetic diversity that you need to introduce new blood. You can enhance certain traits by selective inbreeding. For example, selecting your keeper pullets from eggs laid by hens that go broody will improve your odds of getting broody hens in the future. But with inbreeding you raise the possibility if enhancing traits you don't want, like maybe a physical deformity or loss of fertility. Even accounting for the mutations, all our current chicken breeds were developed by selective inbreeding. Breeders develop grand champion show birds by using selective inbreeding programs, but they have to occasionally introduce new blood to keep the genetic diversity up. You may be able to go several generations without introducing new blood, or your chickens may have something in their genetics where your plan just does not work out well.
My parents kept a self-perpetuating flock, but every 4 or 5 years, Dad would bring home about a dozen chicks from the co-op to bring in new blood.
In any case, if you hatch your own, you will get an excess of roosters and likely more hens that you need. Do you have a plan for how to deal with that?