Pretty much every messenger is built around a central server. Tracing connections to that server is not without hassle but doable with government resources. Now, a Briar-Style P2P Network could work but that has it’s own problems. Central servers are popular for a reason.
how would they prevent me using a chat app they can’t look into?
I dont think they can, unless they get android and iOS to do this os wide. The bigger problem is: will the public care enough to use such a messenger? Will they do it when it becomes illegal to use such a messenger? If not, mass surveillance is inevitable and those sidestepping it for important privacy reasons are easily detectable making them easy targets.
It’s hard to control which Information other people get in a system where many servers share information like posts and comments. Think of it as throwing your post on a public wall. Everyone that walks by will be able to see it.
It’s (relatively) easy to control what information you want to see. Or at least information from which sources you want to see, or not see.