Why would you want to replace the internet at a technical level, which is what the post appears to be focused on?
There's plenty of arguments to burn-it-down at a social level, but building a second technical implementation doesn't get you around those. Having individuals own more of the core doesn't do much when the network level itself is largely neutral to the content that passes through it.
Also the core of the internet is built around big, fat pipes. Those are beyond the means of most hobbiest folks running their own equipment. Without those pipes, traffic will reach bottlenecks easily and usability will suffer.
I'm old enough to have had one and a Tripod and Prodigy page for that matter. I still don't think the analogy holds up at all. Geocities was a single centralized commercial entity even. People contributed the content and they hosted it, this is still to this very day what traditional web hosting is. What I guess you want is more authentic, personal content?
If AI content is a chief concern, what would be the mechanism to stop the flow of it that couldn't be applied (at a technical level) to the internet as it exists today? Or what human-driven policies could be made and policed better on a new network that nobody truly owns? (hint: this is already the internet)