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).
No, in the 1980s, dissident voices had platforms. They weren't "mass media" platforms but they definitely had radio shows, periodicals and various publishing channels to disseminate their publications and broadcasts. They were incredibly important in those days, and those sources held some amount of power, in that they could expose a story, and effectively force the rest of the media to cover a subject or event they otherwise would have ignored.
This is worse in every way as it /completely/ locks them out the modern market of ideas that is the internet and ensconces prior restraint into law in a way that violates the civil liberties of every citizen, whether they are the publisher, or the consumer.
We have lost control of the internet. Those who have control intend to turn this world back into a fiefdom with their newfound power. They are otherwise working to keep the rest of the population in fear and distracted. I'm genuinely afraid our past luck will fail to hold out. They've spent 20 years to get to this point. I don't see them giving up.