There are bradfords that are cared for their whole lives that pruning, cabling, bolting, the shelter of community, luck and prayers have protected from their inherently terrible structure.
Just today I cleaned up yet another of the 12-15 year old "specimens" bordering one of our customers property.
Windstorms have been breaking these things for a few years now. and we clean them up one at a time. These trees matured without any care and are well, typical in structure.
My recommendation for those mature bradfords not coddled since establishment? 100% canopy reduction, chunk the stem, grind the stump and replace with a real tree.