if you severed all of the rhizomes for the culms that you want and do not let them establish culms of their own, they will die and very slowly rot away.

Once you cut the rhizomes, they die beyond the cut point. Unless these rhizomes were in the ground for long enough to get really established (maybe a year), they wouldn't be able to keep growing, even if you had left them in the ground. Bamboo is not like those invasive weeds that can regenerate from pieces left in the ground. Barriers do generally work...as long as you keep patrolling for rhizomes that either jump the turnstile or manage to penetrate the barrier. My ground is too hard and I'm too lazy and cheap to install barriers, so I keep my bamboo under control with yearly rhizome pruning.