They would love to have a camera on hand to capture spontaneous moments around their young children. But choosing a smartphone is a compromise between buying a low-level phone that is small enough to be operated with one hand, normally leaving you with a terrible camera, or one with a decent(-ish) camera that is a pain/impossible to use day to day due to the screen size.
BTW just using a camera on a smartphone with one hand is no joke; the trigger buttons generally assume a right-handed or two-handed hold. You can test this by operating your phone with your right hand held behind your back.
I'd love to see more UI designs that take into account that some people have non-standard configurations.