It doesn't really matter if they "should or shouldn't" have an expectation of privacy IMO, they already do have that expectation.

> If they were to offer total privacy, is it ok for the public to use chat to get advice on _how_ to commit a crime?

Yes it should be, but it should be illegal for a company providing chat service to respond with anything other than a refusal when doing so.

That detection and refusal should be a private closed loop though, anonymizing any data that will be passed into a training pipeline, or ads targeting. This requirement for closed loop private chats should be mandated by law sooner than later. Otherwise we're getting into very tricky territory where the temptation of alerting on things like pre-crime grows too close.