Let's say that one does not trust ECC a lot, and values confidentiality over authenticity (perhaps simply for the reason that MitM is more difficult than passive eavesdropping and decryption later on). In this case one might use classical DHE for key exchanges, and ECDSA for signatures.
Is there anything problematic in doing so? In order to have high encryption strength, one would use large DH params (16k perhaps) since the classical DHE key exchange is not computationally expensive, and faster ECDSA signatures on the exchanged DHE keys. Further, this combination is not part of the TLS specification (as far as I know), why not?
EDIT: Just to clarify, it appears this is indeed not part of the specification, but I am seeking answers as to why not, or if this would be a bad idea from a security perspective.