In general, the 4-way stop is something that should be rarely used, but is appropriate in some cases. There's a 4-way stop near where I live that I think is very appropriate; the busier road isn't so busy that a stop sign causes traffic to pile up, but is busy enough that if it were given unimpeded flow, the cross street would have difficulty crossing. But installing a traffic light would likely cause longer delays on average for cars, and would also be a bit of a problem as the intersection is at the top of a hill and a traffic light would cause traffic on the main street to back up down the hill (and you don't want people to stop on an uphill if they don't have to).
FWIW, if topography allowed, this would make for a good roundabout spot. But it would take up a bit more space than the (admittedly large) intersection, and the topography of the hill would cause a problem. I suspect that something similar could be said of all appropriate 4-way stop signs, that they'd be better as roundabouts if space and/or topography wasn't a concern.