I was reading the Permacoin whitepaper at
http://cs.umd.edu/~amiller/permacoin.pdf which got me thinking this question. They require a method of preventing pooled storage. From what I understand data storage is Permacoin's equivalent of hashing power for Bitcoin. So they tied their "proof of work" algorithm to the private key of the reward payout address. This prevents pooling because everyone "colluding" to pool their resources must know the private key to perform the work. So if 100 people decided to pool their resources together, then they would all have to know the private key. So when the pool solves a block then it would become a race between the participants to send the funds to an address that they controlled individually, which effectively negates the benefit of pooling.
Bitcoin doesn't have this "limitation" because the proof of work only depends on the public key. Only the pool operator maintains the private key and the other pool participants trust him to pay out the rewards proportionally.
So here are my questions:
1. Would it be possible to change the Bitcoin protocol to work like this? Is it possible for the proof of work algorithm to depend on the private key of the reward payout address? I think this would even prevent "pools" like p2pool from working as well. It would also squeeze out small miners who would never see a payout in their lifetime.
2. If it is possible, then would there be another protocol change that could bring the small miners back in? Some way for them to get proportional rewards without pooling with other miners?
3. In either case for #2, would this be good or bad for Bitcoin?