It is too abstract a problem for most people to understand the value of data because they just look at the presumably uninteresting data they share. But you can consent to such usages of course. I don't want foundations or NGO to own the data neither, this would be exceptionally horrible. Perhaps because I have horrible foundations in mind right now, but there is a lot of bullshit in this space. Overall it would be a worse situation than the status quo. I agree that banning isn't an option too. But a mechanism to withdraw consent of your data being used for AI training seems reasonable.
I feel there has be an easy way for to earn digital rights, digital equity , digital money for the artistic minds in this digital era which is proliferating very fast.
We need to find a way to enable benefits to all the data contributors. I find the Gitcoin way of developing a product as great way to engage community and enable folks with a equity enabled token . Something similar should happen with data providers too.
Foundations, NGO or public dataset orgs can just sell the token in the market to people who want to use the AI and benefit from it.