The original Internet wasn't built on trust, it was built by the government for military purposes in the sure and certain knowledge that the only people that had the ability to mess with it knew what was likely to happen to them if they did.
The Internet was later coopted by groups of academics who didn't really have to worry if their communications were intercepted because they were pretty much public anyway and had nothing really to gain from abuses such as faking BGP route updates. Trust wasn't required.
The public, commercial, Internet may have had an illusion of trust, based solely on the fact that nobody historically worried about it. That doesn't mean it was based on trust, if means any trust it enjoyed was based on ignorance.
Trust in the Internet is in any case a wider issue than who is listening in. It's also knowing what really happens to the data about you provided voluntarily that gets hoovered up by all those online services chatting to each other behind the scenes.
Nor is it merely about the Internet - it's about your phone, your car, your smart watch, your contactless payment card and all the other things that can be enabled by technology to spy against you.
There isn't a technical fix to all of that, some of it has to be a political fix.