The problem is not whether it's private or government.
The problem are multiple, but the main two problems found in an experiment with public facial rec. in an Italian city (Como, and now in Udine, too) are:
* municipalities should not have the power to conduct an investigation. That is a clear breach of the separation of powers. At least in Italy every access to information for investigation must be logged, from why it was collected to who requested access to it. Most of the initial deployments of facial rec are way too broad
* Our laws require consent before gathering information on people, and biometric has even stricter rules. Just going around in public is hardly giving consent
You do in Europe. You essentially own the copyright to your face.
If the ban doesn't prevent 3rd party data access the above will likely happen.