X.509 CSR: Why does CA remove signature?
If the CA issued something with a CSR as the dominant part of the To-Be-Signed field, it wouldn't be a X.509 certificate and hardly any existing software would know what to do with it. I guess the original CSR could be added as an extension, though.

Therefore, I suppose you are really asking why the X.509 certificate format wasn't originally specified to include the signatures of both the subject and issuer. I guess the reason was that if a PKI application trusts a specific CA, then that application trusts that the CA adds correct information (pairing a subject with a public key) in all of the certificate fields before issuing it. Adding the signature of the subject wouldn't add anything security-wise.