> It might be my imagination, but I seem to recall nearly all, if not all, 4-ways marked as such with a small rectangular placard below the stop sign in Virginia.

This is the key problem. Whether an intersection is a 4-way or 2-way stop sign changes the right-of-way of any person with a stop sign. (If it's 2-way, I must yield, but if it's 4-way and I've reached the intersection first, I have the right-of-way.) It is crazy that in the US, a person at a stop sign can't distinguish these two situations for certainly without looking to see if the other direction has a stop sign.

(Similar complaints can be made about flashing-red and flashing-yellow intersections.)