Well in Estonia (an EU state) this certainly doesn't happen with any regularity. The tax authority has the possibility to ask for bank statements, but they are required by law to inform the account holder of this check up. It only happens for cases where you're already under a tax authority investigation.

I know though that this is the case in more government-happy states like Denmark, where the banks send this data more liberally.

Anyway even if all the data would go automatically to the tax authority, that doesn't reveal anything. The company would be paying tax properly on all of this, that's the whole idea of laundering. To get the money into the legal system.