In my limited anecdotal experience, since we're talking bikes with single front and rear sprockets . . .

My bike with a 3/32" chainring and rear sprocket turning an IGH with a 3/32" chain, made occasional weird and snappy chain/sprocket noises when I first got that bike. As an experiment, the problem went away when I angled the rear wheel/sprocket toward the front chain ring. The problem went away for good when I installed a flat rear sprocket and aligned the rear wheel straight again. It turned out that the original rear sprocket's dish caused a bad chain line with a single speed chain (less side "flex") and I couldn't flip the sprocket's dish due to the chain hitting the 8 IGH cover.

Now, my other bike (single speed) came with a 1/8" chainring and chain, but a 3/32" rear sprocket. It has a good chain line. I'll let you know when I start to see wear problems. That might be a long time considering I'm not a high mileage rider.