(I've never developed anything with blockchain or torrents, so my apologies if there's a technical reason why this sucks.)
If I understand Pirate Bay and other torrent sites correctly, they don't host any content. They just index what's available P2P.
I'm not sure how large that index would become, but I could imagine chunking the index itself out so that it doesn't take much room on any one user's machine.
The chunking of the index could theoretically be done in such a way that no individual chunk would have any useable information, so no individual user could be accused of linking to illegal content. (I think that's conceivable? Again, not sure.)
(Please note: This is pure hypotheticals. I have zero interest in seeing such a system come about.)
With hosting, you can either have it centralised so users are anonymised from each other (but it’s easier to take down centralised repositories) or decentralised but where users can see each other (but then it’s easier for copyright holders to go after individuals). You can’t really have it both decentralised and anonymous.
To be honest, I wonder why western governments don't ban cryptocurrencies.
They make tax collection harder and help criminals collect money. Plus that would be a blow for countries that are investing tons of money in it eg China, which is destroying the rest of the world, economy-wise.
There is the possibility that western governments are already under Chinese influence, I guess, but I wasn't definitely expecting BTC to survive so long. Especially because governments are not even benefiting from cryptos.
Then when it becomes the modern equivalent of Usenet/IRC/Napster/PirateBay, people will just shrug and say "don't blame the protocol".
The demand exists and the technology exists, but nobody has put them together yet.