What's more popular doesn't necessarily equate to what's more reliable. There's nothing wrong with double triggers from a reliability standpoint. Matter of fact, they have an edge over single triggers--much as pumps have a reliability edge over autoloaders. The fact that you don't see many DT's or pumps in competition these days doesn't have anything to do with the fact they don't work--any more than the fact that you see more automatic transmissions than manual means that stick shifts don't work. If your car with an automatic transmission won't start, you won't be able to solve the problem by popping the clutch. If your single (inertia) trigger doesn't work, you're stuck unless it's selective and you flip the selector. Much quicker if your front trigger just goes click to go to the back trigger.

Problems with DT's have nothing to do with mechanics. The system worked well for a very long time. The problems are either with the individual shooting the gun, or with external conditions--like maybe very cold weather, not enough space for a heavy glove, something like that. Problems with single triggers, in contrast, are almost always mechanical--unless maybe it's shooter error choosing a load that's not heavy enough to actuate the inertia mechanism, or not seating the gun tightly enough to do so. Shooting in a skeet league yesterday, I apparently trapped the trigger on my Parker Repro a couple times. Cold day, wearing gloves, didn't get off the 2nd shot at doubles. And the Repro trigger is mechanical, so it wouldn't be a question of not resetting. Impossible, on the other hand, to have that happen with DT's. As long as there's enough space between the triggers, you can get to the rear one and make it go bang.