I just don't believe they would be able to roll it out. A lot of messaging services won't implement chat control. If half of the messaging apps are getting blocked, people will get angry.
There will be massive backlash towards EU. Texting is just so embedded to the daily life, if the EU causes inconveniences or trouble with texting, this might create massive anger. It could start off Brexit-like campaigns in some countries.
I'm not saying that it is impossible this is going to be implemented. But I think it's just some bureaucrats dreaming.