Why should my certificate signing request be signed by my private key?
Even if I obtain a bogus certificate out of someone else's public key, that is going to be useless, since in SSL the communication can happen only via session key. That session key will be available to me only if I have the corresponding private key for the public key I used to get the certificate for, for the client (or the other party) is going to send the session key encrypted using the public key and I can decrypt it only if I have the corresponding private key.
What then is the need to prove to the CA that I own the private key for the public key I am requesting the certificate for?