Polson, the weekly test is for the VHF/800 system. The HF system is a regional link, and I don't know of any regular test schedule for it. Note that those freqs are not part of the amateur allocations, I guess they are government allocations. Our EOC put some effort into getting the HF system operational last fall, maybe it's a FEMA requirement.
John, there's a case to be made for random or semi-random tests as being a better check of preparedness, but I see your point. Most emergency managers are multi-function people who might find it difficult to wait by the EOC radio for 30-60 minutes waiting for the weekly test. On the other hand, it would be a good time to do a regular systems test in the EOC while you were waiting, or catch up on some paperwork, something like that. It's only 1 hour a week, max.
Mark S.