This seems unlikely, but if you thought that the site that you believe is github.com might be responding to you with tampered data, and you wanted to allow an i

This seems unlikely, but if you thought that the site that you believe is github.com might be responding to you with tampered data, and you wanted to allow an independent third party to view the bi-directional traffic flowing between you and that entity, then you might want to communicate without encryption. (it could also reduce encryption and decryption load at both endpoints, and if you have other means to enforce content integrity then the channel itself does not have to been encrypted)