Things like this will test how much EU citizens value their privacy. Of course there will be some sites they will not be able to visit but time will show if they are okay with that. These rules are very similar to rules limiting loans. No matter how desperate a person is and how low credit they have, in the US you can't give them a loan for above a certain amount of interest. That could be terrible for a poor person…
I mean, mild annoyance is nothing compared to the annoyance of war thorn continent, I wouldn't bet too much on the destruction of EU or even withdrawal of GDPR