To say that we would be safer without stop signs is like saying we would be safer without seat-belts. It is demonstrably false.
I lived in Germany for close to seven years. The typical town doesn’t even come close to having the same number of stop signs we have here, yet it is much more rare to see an accident at an intersection over there. Their premise is simple: if you are on a primary road then drive through the intersection, if you are not then wait, and if neither road is a ‘primary’ road than the car approaching from the right always has the right of way regardless of who gets to the intersection first. Very easy.