It doesn't.

1. There's already pages where people can inscribe random text and images into blockchains: https://cryptograffiti.info/

2. Researchers found that the Bitcoin blockchain already contains presumably illegal content: https://blockchain.comsys.rwth-aachen.de/

Excerpt from paper #2 on that page:

"we consider the remaining three instances objectionable for almost all jurisdictions: Two of them are backups of link lists to child pornography, containing 274 links to websites, 142 of which refer to Tor hidden services. The remaining instance is an image depicting mild nudity of a young woman."

As for who is hosting it ... even though illegal, blockchain mining is still very profitable if you have subsidized cheap electricity like in China.