This somewhat assumes blockchain can also deliver on privacy. Perhaps full encryption of the data is enough. But who is paying for all the nodes?

Another way to do this without the blockchain is open standards (think… HTML for example!) and software that lets you export. Where possible run this software open source on the desktop or as an open source web app. Think Photopea as the pinnacle here.

The blockchain or no blockchain approachable both suffer when you have a data format per app locking you into that app anyway.