That's an overly simplistic situation. Maybe the bottler bottles for multiple companies. Maybe Coca Cola could redesign their own bottles to target specialized

That's an overly simplistic situation. Maybe the bottler bottles for multiple companies. Maybe Coca Cola could redesign their own bottles to target specialized bottle-filling machines, and Coca Cola would have enough volume to use all of that bottler's capacity. But the bottler won't invest in the machines, because they don't want to only bottle Coca Cola products. And absent that, the bottles never get redesigned and the efficient machines never get bought. And absent that, Coca Cola is more expensive than it could be. Or maybe absent an integration, the product offering isn't what the market really wants, because it doesn't want to have to combine two things. Vertical integration can breed efficiency. It can also breed monopoly, but you need to address the iron man if you're making an argument.