For your example case, I don't think it's worth trying to reuse CSRs. However, for a large diverse team Apple iOS developers (like I have) there is a good reason to do this. We create (actually, ask Apple to create) all our signing certs and push certs off the same private key. That way we can all collaborate easily on our 85+ apps. For this reason, we keep a single CSR lying around and always use the same one for as long as the key is valid.
As far as I know, there is no reason to repeatedly generate CSRs from a single private key. I'd love to be corrected if I am wrong.