Jerry brings up a few great points.
One major advantage of rivets is that the peening operation will swell the body of the rivet to fill the holes. So that does greatly reduce the possibility of the parts shifting. The riveted joint is strong in shear but not in tension.
Riveting is a less expensive manufacturing process than a bolted joint. You only have one piece to insert and one tool to complete the operation. Think of a simple press type tool (hydraulic C-clamp) to assemble it. A rivet works better in thinner joints where you cannot get enough bolt stretch to maintain clamp force.
A properly designed and assembled bolted joint should not move. The friction between the parts that is created by the clamp force (bolt tension) prevents movement.
