Total rough draft
The problem with the internet today (aside from non universality of IPv6) is the way people pay for access. Internet consumers pay generally for a certain bandwidth, possibly a data cap if they're using mobile internet. Internet "producers" (e.g. those running servers) pay pretty much the same way, though a data cap is more common for them. ISPs handle the magic, connect the consumer or producer to the various backbones, and we get our connections. Since the 90s, consumers have become used to flat fee, unlimited internet.
Consumers don't think much about the different possible paths their data can take, and if they bother to inspect their connection, it is only to test total Mbps. Yet the fact is that different internet services take up bandwidth and require varying degrees of Quality of Service (QoS). Hence the current fight over "Net Neutrality" which basically is between large ISPs who want to charge service providers like Netflix for high QoS delivery of streaming video. Partly this is of course motivated to shift the cost of installing faster networks on to Netflix et.al. since consumers react negatively to increases in the cost of internet services, and of course many ISPs also offer their own competing streaming video services, which by the way may actually use network resources more efficiently if the ISP is able to put caching servers of their content near their consumers in their own network.
The ones getting the shaft if "Net Neutrality" regulations prevail are those internet users who don't stream tons of video-- they are paying for the same connection speed each month, which may be very dear to them to e.g. download PDFs to read, or even download videos to watch later, but they aren't benefiting from network infrastructure necessary to deliver streaming HD video. Conversely, if it is rejected, then those who watch streaming video and those companies (aside from ISPs) that sell streaming video will lose their subsidy and have to pay more for their use of the internet.
Some of the problems that exist now:
So what's the solution-- the payment model of the internet needs to change. The routing protocols of the internet need to be adapted to use cryptocurrencies/tokens to pay in an instant and seamless way for data usage and quality over different routes. Settings in ones web browser and operating system would handle what speeds and QoS are used for different services, even down to settings for specific websites. Things like system updates or large but low priority downloads would take place over cheaper routes-- those either slower or offering lower QoS. The fact that connecting to view a streaming video would cost more would make consumers consider alternatives-- like downloading the movie instead. I mean-- how hard is it to decide: I want to watch "The Gods Must Be Crazy" tonight, download the movie while you're eating dinner, and then go watch it? Are people not able to plan just an hour ahead? Then those ones should pay more.
And since there is this seamless payment system that is part of the routing on the internet, then the websites hosting content can have their own price to. You don't need to jump through registering to get past a paygate-- just automatically you try to access an article, it exceeds the maximum you're willing to pay for an average webpage view (e.g. this might be $0.0028, average amount websites serving advertisements get per impression, plus some smaller amount that is the average cost/MB of the data), so you get a prompt in your browser: "This site wants to charge $0.20. Accept? Always accept for nytimes.com?". Just now you don't have to pay for as much bandwidth to load pages as fast because they don't have any ads.
Likewise the payment system doesn't need to be one side only paying for the bandwidth. Online retailers might choose to cover most of the cost of consumers connecting to them. Likewise political organizations, NGOs, etc. might pay-the-whole-way for someone to connect to their site to see their message. Video chat clients would likewise include some options as to how the cost of the connection would be split.
And by-the-way-- you're worried about privacy, about censorship, etc? Don't you know how top heavy the internet is at present? The internet becomes more resistant to censorship the more possible routes exist between the consumer and the server. Having payments built in to the routing protocol would mean:
I hope this inspires some people out there. I have a superficial familiarity with these technologies-- e.g., I know they exist, what they do, and can imagine some more uses for them. I'm certainly not knowledgeable enough to rewrite lower layers of the networking model to support micropayments through cryptocurrencies. But such people exist, so there is hope.