That might be fine in a world where every country is on-board, but now that the internet exists, countries with anonymous free speech will come out ahead.
Here's a darker thought: The pre-internet US and UK had a crime problem. Crime was spiking through the 1980s and 1990s. People were disaffected, jaded, they felt that the halls of power were captured by corruption and their voice didn't matter. This is the environment that gave us the original Robocop movie, a hyper-violent celebration of the commoner over both criminals and corrupt government institutions.
The internet economy revitalized the western world and helped us pull out of the crime doom spiral. Without that miracle, we were probably on track for ruthless Duterte-style governments, if not something worse like fascism.
Anyway, I predict that the EU will stop short of actually passing this into law. They're not stupid, and they just want "good boy points" for trying (not from the voters, of course, but people with real political power).
In no way do I support this surveillance society, or legislation, but I just wanted to make a casual point. I'm from a country where the internet first came through universities, and I was privileged to be there at the time. Those early days when it was just university students (and other staff) communicating over IRC were, nostalgically, wonderful. And everyone knew who everyone on IRC actually was in real life. Sure, there were the usual flame wars and some trolls, but it felt personal and, just good.
I'd love to go back to those internet days - bit of course I'm aware that is an elitist attitude, because I was part of the "in group" at the time.
I don't know about you, but I think I prefer the knock-on effects of internet-for-everyone.