Antarctic DHD

So I am relatively new to the franchise, so forgive me if this is a dumb question. Why(or is it ever explained why) wasn't the Antarct DHD not sent and used at Cheyenne Mountain? Would it not have been way simpler than the slow computer program? I'm only at the end of season 3 and I feel like there's been *many* times dialing out needed to be much faster than

Chevron1encoded ...........................................................

Chevron 2 encoded...........................................................

etc.

Where as with a DHD they have it opened in less time than it takes 1 to be encoded in Cheyenne.