I may be being thick so let me reiterate what I think you are saying.
Because we destroy the drones; the Queen made them for a purpose, to swarm and split herself from the hive, to allow a new Queen to take over the old hive. By destroying the drones, the Queen needs to make more drones to replace the lost ones, therefore taking workers from honey, pollen production to rear more drones to carry out the Queens plan?
The nurse bees tend the larvae and will only go out to forage once the reach a certain age, but instead of attending more workers they are re-rearing drones?
I can sort of see that, but if the drones tend to carry Verroa, therefore by inspecting drone cells/larvae (a small percentage), then the health of the hive can be preserved and Mites dealt with before they become a problem so the argument becomes a moot point - chicken and egg scenario
Personally I would not have had drone cell frames, just let the queen and nurse bees attend to making drones as they see fit, but at the same time if there is an infestation, nipping the problem in the bud may well save the hive collapsing still allowing the Queen to swarm off and a Virgin Queen enough genes in the pool for diversity.
I would not cull all the Drones but a sample needs to be done to check hive health. And prevention is way better than losing the whole hive