The real problem is who owns your data. Because if you use Word or Photoshop, your files are locked inside Word and Photoshop. And this is still true if you use FOSS alternatives, because there's only very limited support for metadata-aware sharing between applications of all kinds.
It would be super-useful to have (for example...) seamless links between text editors, web design applications, web hosting systems, and even video editors and ebook publishing tools. But that's not where we are now. There's some limited interchange, but most cross-domain transfers are difficult and fragile, and some are impossible.
Cloud is just the online version of the same model. When you have proprietary control of user data through proprietary file formats which actively frustrate open sharing of data between applications, it doesn't matter of the data is stored locally or in the cloud. It also doesn't matter if you're using a mobile or desktop UI.
The FOSS people have always been looking through the wrong end of the telescope. The real revolution would be open data which is wholly and exclusively owned by users (or user groups for collaboration) and loaned to proprietary software for specific limited tasks.
Which is the opposite of things work now. Applications and products own your data and they let you access it - but only if you ask them nicely. And - increasingly - if you pay annually for the privilege.
So containerisation or self-hosting or whatever is a non-solution unless it also gives data back to users.
Which is also why the fragments idea won't work. There's limited use in trying to automate or manage or otherwise AI-ify access to data that you don't truly own anyway.
In fact a new kind of shared Internet would be a very useful thing. But it would need a ground-up redesign of everything, including browsers, mobile apps, desktop applications, operating systems, search, and the financial and legal frameworks surrounding them.
I'd love to see that happen. But right now in 2021 it just doesn't seem likely.