The problem with that framework is that even if you believe the EU Governments are the "good guys", it's not going to be just them who get access to the data.

The problem with that framework is that even if you believe the EU Governments are the "good guys", it's not going to be just them who get access to the data. It opens it up potentially to anyone with the means to infiltrate these systems - rogue employees of the companies running the messaging and cloud services, cyber criminals who will be able to hack into them, foreign states who will be able to hack it (we very recently saw this how China had infiltrated CALEA backdoors into telephone systems around the world for many years). Which of course is part of the reason that companies are so on-board with end to end encryption in the first place - being able to ensure that rogue employees can't access customer's private messages and files, and that if cyber criminals hack in and infiltrate data that there are no encryption keys accessible is a huge benefit to them - but the moment you try to open it up to "lawful intercept" you open it up to all the unlawful intercept too...