Couldn't ANWR be a form of "strategic reserve".

Might be, but don't you think we should explore it to at least determine the extent of these reserves? And have infrastructure in place that allow these reserves to be used. A "strategic reserve" something you could get in a relatively short period of time. And a mad dash to explore than exploit these resources could be more likely to damage that precious environment some are extremely worried about.
"Environment? Who care about the environment, this is a matter of national security" - might be an excuse not to follow all regulations designed to safeguard the environment. And in time of serious war and acute need; the Executive Order would be quite simple: just do it as fast as you can; we need it yesterday. "Regulations? Forget about them. Pipeline? Well, I guess it might needed in longer term, but we need to get every truck and tanker up there. Possible, we could lose a tanker in this weather? Well, we got more than one, right?"

Get the picture?