An interesting thought: what's the lowest speed limit sign you've ever seen?
I've seen 5 MPH in parking lots, but never on an actual road. For official road signs, I virtually never see anything below 15 MPH. I'd be pretty surprised if this was actually the ideal driving outcome. There has to be some intersection at which 5 MPH and a yield sign is the ideal arrangement.
But given how traffic laws are enforced, and how people tend to ignore low speed limits, it's not a very practical arrangement. Instead, stop signs go in everywhere that very low speed limits are required.
(I'm still vaguely wondering whether a lot of people in this thread have ever driven somewhere very rural. Gently rolling a stop sign at an intersection with a mile of visibility and no one else around is not some wild risk.)
A lot of times, they will be placed as a form of speed control. The MUTCD has requirements regarding the use of stop signs, but they don't appear to be followed most of the time. Otherwise, we wouldn't have nearly as many stop signs at intersections where there is plenty of visibility of cross traffic.
Of the two parts pertaining to complying with a stop sign (first stop, then yield), the second is far more important than the first when it comes to avoiding a collision. You can certainly come to a full stop and subsequently fail to yield and then collide with a pedestrian or vehicle. But even if you don't come to a full stop and do yield to a pedestrian or vehicle that has the right-of-way, you're not going to collide with them.