[montzark]

Maybe technical solution to this without backdoors would be to encrypt everything twice and store both?

One is for intended target and second time with public key provided by law enforcement.

And perhaps there should be a third independent actor who would hold the private key (in hardware without extraction possibility hopefully) and on request basis would decrypt something for law enforcement and provide supervision and statistics for citizens. Ok one problem would be then that if that machine breaks there is no way to decrypt anything encrypted for that public key :D.

[rocqua]

This is a back-door, since the public key will give you full access to plaintext.

Moreover, how do you audit whether the second cipher-text exists, and whether the second cipher-text actually decrypts to the same plain-text as the first?

There are plausible schemes for creating a common second actor that can access communication with a warrant. But they aren't this simple, and they tend to come with large complexity downsides.