That's why not giving them ability to copy data, allow them to use that data only on your device and send aggregated information back. So they cannot copy the data
Like you can have decentralized web now, you can host your video on your server. Maybe even p2p. Just the reach would be probably minimal. And you can have your own bitcoin wallet. I was downloading chain to my wallet ten years ago and it was slow. Most people will chose some centralized service even for crypto.
In decentralized world, everyone can build their models, host them and train them on user data. But since, I wouldn't want my data to be used for any other purpose, I don't want them to make a copy of that data. So they send their models (after taking my consent) to my device, train it locally and send the aggregated model back.
If you want some personal data to show up somewhere be it a name or avatar it has to leave your device. At that point someone can and will copy that data. If there's value with associating that data with your activity someone will do it.