Fitness walking shoes should flex at the forefoot, as walkers should push off with their toes. A shoe that bends at the arch does not provide the platform they need. A shoe that doesn't bend at all is unacceptable. Unfortunately, many shoes marketed as walking shoes do not flex at all. They are unsuited for fitness walking.
The photo shows a running shoe that flexes at the forefoot and is suitable for fitness walking.
Motion control shoes and stability shoes will be less flexible, as they have medial posts and other construction elements that aim to keep the foot from rotating too much during a step. Runners and walkers who need motion control have to sacrifice some flexibility in their shoes.