Snap caps are a necessity for rimfire weapons...break the firing pin on them, possibly, but mostly it's to prevent peening the firing pin against a piece of metal harder than brass, which will wind up making an edge on the firing pin that can puncture the case, instead of just striking it.
As far as snap caps in center-fire handguns and rifles, they're not a necessity. Any modern firearm can safely be dry-fired without fear of breaking or harming the firing pin or mechanism. On some autos, like a 1911, you really shouldn't drop the slide w/out hand-cycling it, on an empty chamber. The weapon was designed with the cartridge slowing down the chambering process, preventing battering the barrel hood against the slide. In theory, dropping the slide on a dry chamber enough times will cause damage to the barrel hood...have I ever seen this, no, but just looking at the design will tell you something bad might happen if you do it too often. That's the only reason I use snap caps; dry function runs, to make sure things extract and eject.
To put it another way, the military dry-fires their rifles and pistols all the time with no damage to them. You can bet every major military power does it, from the Chinese, to the Russians, to the Germans, to us, etc.
For shotguns, yah, I'd imagine SxS or OU shotguns need them...totally different mechanisms. That'd be about it for necessity, though.