Given the amount of compromising photographs obtained through hacked smartphones, there is not just a market for simple point-and-shoots but even for instamatics which print out a photograph just taken and do nothing else with it.
I also want a point-and-shoot (which does not mean more than a camera that picks aperture and speed unless told differently) because the controls are right. For the same reason, people buy electronic keyboards even though you could do the parts of the electronics on a smartphone.
The last film point-and-shoot I bought (an Olympus Stylus Zoom whatever) had an optical 3x zoom and the necessary controls for using the camera. So even when a modest zoom range came at non-trivial price in image quality and/or money (you basically had to accept springing for ISO200 by default), it was compelling enough to factor at least in some people's buying decisions (and yes, I knew that the reviews for the zoom version were decidedly less enthusiastic).
The ratio of people carrying a point-and-shoot "just in case" was actually not all that large even in the age before smartphones. Carrying a camera usually was coupled with habitually using it rather than keeping it around in case one needs to document some rare occurence. Of course habits were additionally shaped by films having a limited lifetime and a minimum practical size of 24 pictures. For shooting once a month, this would have been a hard sell.
People will lean towards smartphones more for creating photographs for sharing rather than hoarding. If the photographs are just for you, the incentive to have a camera just for making your photographs is larger.