It's not quite that simple: it's not just a weight based on voting, since that's obviously gameable by anyone who can accumulate enough coins to guarantee a win on a single contract, but it's a weight based partially on how each voter reflects the majority in all the other contracts. So anyone trying to corrupt a particular contract has to deal with the combined opposition of everyone who wants weight for every other contract.
Bitcoin does rely on an identity system; it's called proof-of-work. It counts hashing cycles rather than humans, but it's close enough since the final goal is decentralization and not perfect equality. Here proof-of-work or proof-of-stake are also equally necessary for bootstrap purposes; otherwise you can use whatever mechanism nodes use to get into the system in the first place ten thousand times instead of one time and thereby massively magnify your reward.
TLDR: proof of voting is a good consensus algorithm, it's not a good distribution model.
