I don't want to sound too harsh, but it doesn't seem like you know what hashing in Bitcoin does exactly.
https://en.bitcoin.it/wiki/Proof_of_workEdit:
To be more specific. You're talking about getting consensus over some abstract data while using "hashes" without a blockchain. The reason this doesn't make sense is because consensus is about the ordering of transactions over time, so when you remove the blockchain you're just talking about a piece of data you're spreading around and hashing "it" doesn't do anything for us.
It's like saying, "If I send an email to 100 people, how many hashes do they need to perform before we have consensus that they received the email (or that the email is correct)?"