A good reason to own a digital camera: Waterproof
Being waterproof is actually one of a few reasons to own one of these.
Seen above is the Olympus Tough TG-6, a proper waterproof digital camera. True, you can go cheap with a waterproof digital camera, but if you do, you probably won't be pleased with the cheap stuff. This is one of those instances where you truly do get what you pay for.
Taking photos with a smartphone works in most instances, but when Mother Nature is introduced to the situation, that's when a phone is just a useless plastic brick. Yes, the smartphone waterproof case exists, but that doesn't get the job done because it's not tough-built.
The TG-6 is both waterproof and tough. And what does "tough" mean here? Waterproof, dust-proof, shock-proof, crush-proof, freeze-proof. That's what it means. Your phone can't be all of these things, but the TG-6 is.
Real world situations where this actually matters
Ordinarily, the way one of these is marketed is by showing outdoor adventures. Biking, hiking and that sort of thing.
Where having one of these actually makes more sense is in manual labor environments. Construction, working in the yard, working on a car, and so on. The places where you wouldn't dare take a phone is where a camera of this type can go to take the photos you need.
Note the metal loop on the side. A roofer could put a strap through there, attach to the tool belt and have a camera at-the-ready whenever he needs it. That's actually really convenient.
Owning one of these is for the same reason one owns a G-SHOCK watch
A complaint I've had about smartphones for years is that they can't handle life, so it's no wonder Otter cases sell so well. And for environments when the Otter case isn't enough (which happens more often than you think) where you need to take a photo or record video on something that won't break, that's what the TG-6 is for.