Performing serious tasks on mobile

I have a theory: A large percentage of users are reluctant to do something too serious on their mobile device. The smaller screen and lack of control here induces a sense of unease. It's possible that past experiences with low quality apps could also be a factor.

When it comes to doing something on mobile, adoption is hard. Yet, once passing that hurdle, retention should be high.

It's possible that this applies to 'desktop first' users only. For a kid who has always had a smartphone but rarely touches a desktop, things would be the complete opposite.

Familiarity could increase a user's tendency to perform a complicated task on mobile. But as they get used to the mobile app, will users stop resorting to desktop applications? Or will each app always have particular roles?

Are there - and will there always be - particular use-cases exclusive to desktop and mobile applications? Does anyone know of any research related to such issues?