Periscopic sights seem like they’d make the most sense for tripod-mounted weapons, which don’t need a well-positioned human body attached to keep them stable and on target. The early periscope rifles of World War I weren’t especially accurate for that reason — and because they were built in the trenches with the equipment at hand. I would expect modern optics and machining to greatly improve matters.

I find the idea of a curved-barrel gun rather silly, but a slightly periscopic sight that let you shoot around a corner — rather than over a trench — would let you keep your shoulder behind the gun but your head behind cover.