Generally, the hen need not loose feathers to expose the brood patch you are feeling. The skin their becomes extremely stretchy and she has muscles that allow her to open the patch as she settled down on clutch of eggs. When you find feathers in nest of such birds, that is because she pulls them in from immediate surroundings to line nest. Seldom do I find any feathers in a nest but do find lost of other fibrous materials. Exception to that is when lots of feathers are on the ground near nest site.
Brood patch does facilitate transfer of heat. It might also help keep eggs from drying out.
If you can sit by a brooding hen for extended lengths of time so you can see that she does a lost more than just sit there. For me the first thing noticed sounds and they are not vocalizations.
