this would involve verifying a LOT of shares
Note that shares are artificial concept, present in mining pools. In the Bitcoin network, you have valid blocks, or invalid blocks. Any block that does not meet the target is considered invalid, even if all included transactions are valid. Miners are rewarded only by mining pools for those invalid blocks, because they meet some lower difficulty, set by that mining pool.
I am aware of this, the purpose of recording shares (accepted / valid shares to be more specific) would only serve to have a recorded proof of a miner's hash rate. These shares proofs would only be used if they discover a block, and could then be used to prove that up until the block was hit, they solved a certain amount of valid hashes per unit. Its also a work in progress theory and not implemented anywhere yet as I have said.