If we learned anything from the past it's that crypto works and can be deployed if it integrates without users noticing much and if the computational and speed overhead is small (or negative, which in the HTTPS case it often is).
McEliece ciphertexts are unusually small for post-quantum cryptography. The small ciphertext size can be much more important for total traffic than the large key size.
McEliece is relatively fast and has really fast implementations in hardware, so the speed is less off a problem. It does just binary vector operations. Encapsulation is just one pass.
There are plenty of middlebox devices on the Internet that will drop your traffic if you send anything HTTP over them that they don't understand. So you're kinda "locked in" in not deploying new protocol features. Encryption provides a way out of this.