As I understand it, Elliptic-Curve Cryptography is used in the verification step of a transaction (i.e. when creating a digital signature), but not in the creation and security of a 'block' (when assigning a nonce to a hash value with a set number of zeros). Why do we use ECC when validating the initial transaction request, and not when validating the block? Or to flip that around, why not just use Cryptographic hashing in the validating transaction step (and not use ECC at all)? I know hashing is used on the message component during the validating transaction request, so why not use it again for the whole digital signature?
My understanding of blockchain is limited, so upfront apologies for any unclear language!