https://en.wikipedia.org/wiki/Clipper_chip
It's a tough problem. Leaving aside the question of "do we trust the government with it?" That kind of thing is a genie that you can't put back in the bottle. Edward Snowden did not walk away from the NSA with a set of back door keys, but if they existed, somebody like him could.
In 2020 any such tool is on the side of chaos and not order. Today we're having to shut down hospitals because hackers hit the computer. The risk that some people are going to abuse encryption sometime is hypothetical, the risk that people are going to exploit anything that is possible to exploit is urgent.
To detect what end-to-end encryption is used for I suppose that you need to scan and analyse the cleartext.
So...