That is only according to some law systems though. It does not work like that at all in many European countries. For instance in France the employer cannot read any private conversation (mail/message) of the employee, even when using work email. And no internal rule can change that (it is a criminal offense). If the employer suspects a leak of information by the employee, they can read the message in presence of the employee and a union member, and only in those circumstances.
> If the employer suspects a leak of information by the employee
or if they suspect any other illegal activity.
Even in EU countries where arbitrary inspection/monitoring is not permitted wholesale, there are exceptions where regulatory or other legal requirements trump privacy. Though often there needs to be sufficient suspicion of something worth looking for, I still wouldn't count that as a truly private channel (nor would I expect my employer to provide me with one).
But as I said even in those cases the employee needs to be present when the employer accesses private messages, in addition to a union member. So as an employer you cannot just sneak in and check what has been said, it has to be public. Which I think greatly mitigates the risk. It is not a secret conversation like you would have between lawyer and client but it is rather private.