Yes, initially you might be able to catch a few bad guys who don't switch to the new service quick enough, but soon enough, all that is left is the ability for police & co. to read private messages of a population that is mostly innocent.
But that a ban must fail doesn't follow. E.g., requiring passports for travel was a WWI development, and supposed to be a temporary restriction on freedom; the practice was supposed to end after the war, and they had some kind of international meetings about it, and nothing ever happened. Now this has become obscure history that people hardly ever think about.
The line of argument that criminals would be too smart to stay on commercial services is not really robust, as catching just the not so smart ones would be good enough for politicians. There are better arguments.
(The upcoming EU "chat control" mechanism is about similar remotely triggerable client-side fuzzy searching ).
The goal has never been to catch the bad guys.
Look at tor and people running illegal companies through our, some get away with it, but a bunch did get caught eventually.