This thread might be a little cold, I'm just killing time at the end of a long day.
The full time TS people generally answer the oldest questions, usually weighting older threads even if the most recent message isn't that old.
For most TS questions, a majority of the time spent is just in reading the question and getting a handle on the user's situation. A person checking for information completeness would have to do the same thing. Basically, by the time you know that all the info is there, you can answer the question.
We don't really have the staff to have someone doing that full time. You would also be surprised how little it happens. We can answer probably 70% of TS questions without having to ask for information first.
TS here is a hard job. The support people are all really smart and know their stuff. Giving them really boring duties would be crummy. Generally, the less repetitive a task, the more interested a smart person is. We like to keep their jobs as interesting as possible.
If there's anything we could do, it's improve TS people's information-gathering resources so they're faster, more complete, and more clear. It can take some time to really investigate somebody's account to find problems. DreamHost's backend is extremely complicated, and we tend to work on tools that are visible to the user before we improve internal ones.
I can say that, on personal level, the best way to make sure your message is NOT read is to use all caps in the subject, sound angry, and ask things like "WHY IS MY SERVER DOWN?!!?!?" I will never, ever write to you if you do this.
Then again, it's probably a good thing I'm a developer and not a support person.