Most nations are developing increasingly sophisticated regulatory approaches for how the Internet is allowed to operate within their borders. There can be no successor as nearly every nation will have their own requirements, guaranteeing no successor can ever be flexible enough to fit all of them. A successor will end stillborn of hundreds of different regulatory demands: death by committee of 195 nations. Had the Internet originally been conceived in today's environment, with input from dozens of nations, each with their own self-interest at stake, it would have never survived and spread. The sole reason the Internet worked, is because it was initially built by a very small group (compared to the hands touching it today).

Instead what will happen, is haphazard forced customization of the existing Internet. They will beat and punch it into the shape they want it to be domestically. That approach will continue for a minimum of the next 20 to 30 years. Nothing can stop it. The adoption is too high, the investment is too high. Instead of ditching that epic macro investment, nations will bastardize what's already in place and bend it to their own socio-cultural needs or demands. China has already demonstrated how well that can work, how far you can go in molding it to whatever your demands are. If China can do that, others can mostly do what they want with it and will.

The Internet will hyper balkanize, just as most systems from one border to the next tend to (with some exceptions for agreements between large pools like the US & EU). There will never be a replacement system that goes global as the Internet did. It's a one-off - like first discovering a new piece of land nobody had explored before - as nations build frameworks (off their experience with the Internet) to regulate how any digital network can operate, which will make it impossible to smoothly launch a new global network to challenge the Internet. Every aspect of operating socially and commercially on the Internet will get more expensive on average, and especially if your attempt is to operate globally (locally there will be exceptions, countries with low regulatory hurdles and annoyances, but those will be overwhelmingly small nations like an Estonia, New Zealand or Switzerland etc). Internet regulation and control will soar on average, it'll become the compliance nightmare that everything else is that governments get their hands on. That will benefit anybody that gets out of the gate before the barriers get too steep; it will stagnate innovation in most cases and punish anybody that arrives later to the party. Nearly all systems regulated by governments evolve and exist in that mode of suffering, with few exceptions.