The right to private communication is already enshrined in the EU.

Article 7, EU Charter of Fundamental Rights: Respect for private and family life (and probably a couple other sections in there as well).

The problem is national security exceptions. Chat control and other similar bills are trying to carve out exceptions to privacy laws under the excuse of national security.

Also its politically cheap to introduce surveillance or to expand state power, it's comparatively extremely difficult to pass laws that specifically restrict state power.

Privacy laws are well and good, but they exist. The problem is we need to stop allowing "public safety" or "national security" to be a trump card that allows exceptions to said laws, and good luck getting any government to ever agree that privacy is more important than national security.