A double boiler can’t get hotter than 100 C anywhere, until all the water boils off. A directly heated pot can get hotter in spots leading to undesirable reactions.

The double boiler also heats more gently because water absorbs so much heat. You are less likely to overshoot the target temp, especially if someone is watching the pot. A watched pot never boils, so by observing the double boiler you limit its temperature.