Like others have said, they are bred for it. There is a lot of draft blood mixed in there to create the sturdy, large bodies...and that generally also lends them a generally calm demeanor when they aren't "working".
As for retirement. Most the good mares are retired to broodmare status, the studs are retired to breeding status, and the geldings usually fall into 2 categories; those suitable to be re-trained as saddle mounts and those that aren't. The broncs who aren't suitable/safe to retrain but are also not strong enough buckers anymore for the pro circuit are often sold/donated to high school and college rodeo teams to be used as "trainers". These horses are generally pretty easy broncs to ride so they make good beginner broncs. https://www.youtube.com/watch?v=efXNIWWWziQ