To be fair it would be outright unconstitutional in a at least a few EU countries. Then there are the courts on the European level. One way to truly kill it might be to allow Chat Control to go to the end where it actually becomes a major issue on the national level in those countries.
Of course that would be a very, very risk approach...
Losing court cases rarely impresses politicians to abandon laws they have set their mind on. See, for example, the laws about forcing telecommunications providers to retain metadata of their customers. In Germany this got struck down by the constitutional court time and again. But that does not stop the major political parties to start yet another attempt.