I had never heard about geocities, that's interesting, thank you for sharing this.
Now, to elaborate a bit more about what I said, I don't think there is a lack of technical solutions for this, but rather a fully integrated solution is missing. I would like to be able to "seed"/mirror specific content, like articles that I find interesting. Of course, that wouldn't help with content I (or others) haven't read already, but you would be responsible for the content you host, as you pick it (unlike ipfs or freenet, AFAIK). Integrated in a web browser, I suppose it could also "mirror by default", though I would be concerned about leaking user-specific content (so maybe a spec/protocol extension would be necessary for html/http to tell what could be mirrored?).
It occured to me that this was a bit like "boosting" a post in mastodon. Indeed ActivityPub could be an interesting transport mechanism for this, and could be a way to propagate update notifications back. Though I am not sure the content itself is mirrored with the current mastodon "boost" implementation. A mirror index could also be ran over DHT, while a "search engine" could provide the post hashes, and let clients fetch the content from the DHT.
The whole idea is still quite a bit rough, but it surprises me that in 2019, hosting plain text content (more or less a few images) in a future-proof way isn't a solved problem, and we still have to rely on the Web archive. Applying trusted timestamping (by a few trusted third-parties) to the web archive content would be a good start, to trust mirrored content.
If you can't afford a few dollars a year for your domain name, you likely have bigger problems. If ICANN disappears, we all have bigger problems.
Your solution is interesting, however hosting other people's content is fraught with danger. If I ran such a host, I'd assume within minutes I'd be hosting potentially illegal content. How would your system prevent that?
The stuff about kids just reminds me of geocities, TBH. There might be an appetite for something like that once again...