PKI Validation - Usefulness of the public key with the identity certificate
I may have found an answer here: https://devcentral.f5.com/questions/difference-between-root-cert-intermediate-cert-and-ssl-cert


  One more thing one the public key of your server certificate. There is
  the same mathematical relationship as described above between the
  public key and private key of your server certificate. 
  
  It will be used during the SSL handshake. The client encrypts some key
  material servers public key (retrieved by the client out of the server
  certificate) and sends it to the server. It can be decrypted by the
  server using the private key. If the server does not have the matching
  private key it cannot decode the key material and the handshake
  brakes.


But the above may be referring to using RSA for symmetric key transference, which like I posted earlier is generally done by ECDHE these days.

I imagine you'd just be able to take the certificate and use it to spoof a site if you successfully hijack DNS without any validation of the identity certificates public key. Surely it's validated in some way.