I have asked numerous times for the use cases that people are worried/fearful/concerned of - this was an honest enquiry. However, nobody seems to be able to answer it.
Let me tackle the things you mentioned - aspiration, ambition, preference etc.
Yes, it is certainly true that some users would have the aspirations to create their own web-based email (a la Gmail), or file-storage service (a la Dropbox), or their own photo-sharing service (a la Instagram), or their own social network.
However, I should point out two things.
Firstly, the stark popularity of those services would seem to suggest that for most people, they have done the cost/benefits analysis, and figured out it doesn't make sense. The effort involve simply doesn't make sense for them.
The whole point of webapps and most mobile apps is that they store data remotely on some service - I would posit this would be a far greater concern (if you didn't trust the app developers) than whether they knew how often you opened their app, or which features I used.
Secondly - let's be honest, most of us couldn't create our own GMail, Dropbox, or Instagram even if we did have "aspirations, ambitions, preferences" to do so. We simply don't have the technical know-how, time and/or experience to do anything remotely approaching their usability, performance, reliability or collaboration features - or their scale.
There is an enormous amount of engineering effort that goes into any of these services - and most people are willing to buy into the whole web-based application thing, in order to take advantage of that.
I am open to being convinced otherwise - but I have yet to see a reason why the majority of people would buy into web-apps/mobile apps, and have fundamentally miscalculated the cost/benefits.