Right! So (from the perspective of the password alone) the owner doesn't have to care if that password is used only on that site where the horse has left the barn.

If the password is used on other sites, then of course all that protects them its strength relative to the compute resources thrown at it, relative to the time between the breach and discovery.

(From other perspectives, the user does care: like their credit card number was stolen and is being misused.)