I like this list because it will identify the fatal flaws pretty quickly before you spend money on other things. If it's a goner, it's good to know before you spend money on tires and a new seat.
I would add a quick check of frame alignment very near the top, near the fork on this list.
I like the idea of checking on the seatpost at the top of the list. If that's frozen, I usually would just walk away. Some others would be able to deal with it to a certainty, but I can't in my particular environment.
I had written the list as for "new" bikes being built from a frame.
For old bikes, I'd do things quite differently if I was checking one out to possibly fix.
However, you are right, seatpost is still at the top of the list.