Short question: how would they enforce that? What if I use some obscure messenger that nobody has ever heard of? What if I simply use telnet or netcat to send messages to other people?
Telnet? Banned. You now need the EUs approval to use networking software. The only apps that any EU users can use that uses the network interface are those whitelisted by the EU.
That's the only way that this is enforceable. And still pretty easy to defeat, or are they gonna Linux too? Since Linux comes with the source code, anyone could recompile it removing the restriction.
I think these things aren't designed to stop everyone, just most people, non-technical people - not people like us who know how to work around limitations etc.
Criminal would just use the communication method that is encrypted, because it will be known as such. Just like nowadays everyone knows that if you want to pirate you use torrent. And if you don't wanna be tracked you use VPNs and tor.
This will hurt the dumbest of criminals and all the non-criminals.