Make it P2P and content-based, instead of location-based like the current web. Content could be served from anywhere, so DDoS stops being an effective method, and shared peer quality could propagate across the network to ban bad actors quickly.
I spend about 30 seconds thinking about this, so this is clearly the perfect solution with zero drawbacks or tradeoffs.
I know this is tongue in cheek, but I'll give it a serious reply in case someone finds themselves "inspired".
A CDN. What you are describing is a CDN. We have CDNs today and the problem still exists because most of today's websites refuse to operate within the constraints. There is no need for new infrastructure to deploy this solution, we just need website operators to "give up" and operate in a more static way.
Nope, today's CDNs are all location-based, not content-based. The user-agents are requesting content based on the address (the URI), not based on the content-hash of the content. The CDNs might work content-based internally, but the user-facing web CDNs definitely are URL based, not content-hash based.
You might have a point if this was a user problem, but it's not. It's a site operator problem. And from their POV, a CDN provides the exact same functionality.
CDNs are hack, not a solution. Content-addressing would be a solution, not a hack. From the PoV of operators or users doesn't matter, DDoS wouldn't be viable with content-addressing.
I spend about 30 seconds thinking about this, so this is clearly the perfect solution with zero drawbacks or tradeoffs.