Silkie or Polish are what many use for a walking incubator. One of those birds in your flock that you feed and who's sole reason for existing other than looking like a goofy chicken is to brood chicks for you. You don't want to hatch their eggs rather put the productive birds eggs under them...
Line breeding does have it's limits. A decade is good time to bring in new blood to a flock by outsourcing a cock bird. There are flocks that never outsourced and were or are still around for 30 plus years. There is a limit but if line breeding is done correctly that limit may never be realized...