I see many advantages to natural chick brooding: no need for industrial-scale hatcheries, no energy use or fire risk from brooding lamps, and general DIY goodness.
But perhaps the biggest advantage is big grown-up chickens getting to teach the babies how to be a chicken. To wit: this video of Buffy and her chicks when they were about 24 hours old. Buffy had been diligently sitting on the last two unhatched eggs, but it was clear they weren’t going to hatch, so I removed them. Immediately after I took them away, she hopped up from the nest and led her four little ones across their private coop and showed them how to scratch around for bugs.
This is simultaneously so fundamental and obvious (why wouldn’t an animal work this way?) and totally, mind-blowingly incredible. I hope someday to be able to get all if our chicks from natural, in-place brooding.