This is a common mistake w/r/t Proof of Work. It doesn't prevent Sybil attacks. The Bitcoin whitepaper performs slight of hand to say "instead of identities, we'll use CPUs" which are obviously what Sybil attacks are in the first place. One person can own lots of CPUs... (Thus mining operations.)

What it does do is make Sybilers larger and larger shareholders in the network to make it so that the more you Sybil the network the less you'd want to try to damage it.