You're conflating private keys and parameters. The random number that ECDH requires you to generate is the private key, just as FFDH requires you to generate a

You're conflating private keys and parameters. The random number that ECDH requires you to generate is the private key, just as FFDH requires you to generate a random private key (which is also fast). If you were actually generating your own random curves (which TLS doesn't allow) it would be much more expensive.