P and (the fake) P2 can both reply to V with perfectly normalized storage.

But regardless if the protection works against bad actors, it definitely "works" against good actors if you take into account storage prices. E.g. P1 and P2 are two distinct good actors. They both pay cloudProviderA for storage. P1 and P2 bid on the same filecoin storage contract. They store that independently of each other, but cloudProviderA normalize the storage (with their own backup and consistency solutions). But with this protection scheme, since the cloud provider can't normalize, the cost will eventually go up because their normalization margin got erased. Over time, the data storage cost for good actors will go up, while for bad actors (assuming they are possible) the profit will increase.