Why do OP_CHECKSIG/OP_CHECKMULTISIG remove signatures from subscripts?

when OP_CHECKSIG When used, all instances of the signature will be removed from the subscript before being included in the transaction template to be verified. See also step 3 in this great diagram. the same thing is done OP_CHECKMULTISIG.

How can I subscript a copy of my signature? Why should I remove it?