The problem with encryption is that it is bothesome, cumbersome, easily broken or circumvented by silly goofs and oversights, and generally impedes communication. The great enabling power of the internet is that it lets anybody talk to anybody. Encryption is not a good fit for that model.
Another approach would be global mesh routing, you know, mesh together every AP on the planet and hope no spots get left out. But mesh routing, while a nice idea, has scale problems, and we'll probably start to miss the really fat backbone pipes in a hurry.
The appropriate approach here is "government-technical", as in international law.
We have to get governments to agree to keep their hands off of the data that isn't theirs and they don't need for law enforcement and thus is obtained using a warrant issued for a specific investigation. To make this stick people must understand that data collected "just in case" is a liability for everyone involved and thus that not gathering data, while hard, is the right thing to do. Too bad it's hard to enforce. There'll always be some government transgressing, instituting star chambers, and so on.
It may be easier to get governments to agree to keep their hands off of the parts of the internet that aren't theirs. This probably implies some sort of intergovernmental oversight. But I wouldn't pick the ITU, nor the UN in general. They're too much clubs for governments, as if they knew what was good for the people. They clearly don't. Not even the USA, oh whooshing irony. So ICANN is out too, since it is really an US government subsidiary, regardless of what the both of them claim.
Do note that the USA clearly, literally claimed to be the only one country worthy of safeguarding the internet against wrongdoing governments, only to be shown a pathological liar about such things.
Since we cannot trust any one existing government nor any of the existing bodies, the internet will probably have to become its own country. Including datacentres that no longer stand in the country where they're built, but are now in "internet country", and thus entering the datacentre means crossing an international border. With extradition treaties and everything, but so that not one state can impose its law on all of the internet, as, say, Kentucky and iirc Utah did not too long ago.
The effects needed here are that both you can't be held answerable to the laws in any random country other than the one you're in (or do business with, or have some other clear relationship with), regardless of where the hosts involved physically are hosted, and that being held answerable to the laws of your own country (or do business with) becomes easier.
That, or we could try and get a benevolent global, planetary, government, but literally everyone with any shot at that has so far blown it, to the point that I wouldn't trust anybody else claiming to be that good either. So a separate country for the internet it will have to be. It is the simpler solution.