I haven't ever bothered looking at other single inertia trigger guns but probably selector or non-selectors are both designed to just need the safety worked back (on) and forward (off) again to activate the second barrel, forget trying to change the selector over, no need to.

4seventy sums up my take on either double triggers or single triggers on doubles, or bolt actions for that matter, you will need to have the 'presence of mind' to fire your second barrel or reload after a misfire. I have had the odd misfire when using the old SMLE 303 rifles and seen a few others the same and it does sort of throw you a bit when you do have a misfire.

I don't think double trigger users would necessarily have any advantage over single trigger users where hunting any game and have a misfire, presence of mind is going come into play for your brain to accept you've had a misfire and then change to the second trigger or work your safety quickly to get the second shot off. Either one under those circumstances is quite different than getting your first shot away then following with the second under normal circumstances without misfires.
Most of us can fire two shots in very quick succession if we so wish with our brain wired to rapidly pull one trigger twice or slip to the rear for the second trigger.

Interesting how many bolt gun users fire a shot and then hesitate and watch before reloading for a second, they expect the animal to drop with the first and then get flustered if it doesn't and are slow to react for a reload and get another shot away.