This is indeed one of the things cryptocurrencies exist for, but social media denizens around these parts have long conditioned themselves to hate it.
So a rock and a hard place, it seems. Which is more hated; the big data-harvesting corporation co-founded by Elon Musk, or a big bad NFT-hosting blockchain?
For people who are concerned about data harvesting I would recommend something like Monero or Aztec over Bitcoin, though. Bitcoin's basically obsolete at this point, coasting on name recognition and inertia, and has no built-in privacy features.