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).
The authoritarian mindset that thinks that making something illegal will stop people from doing it, doesn't really grok how that just doesn't work.