Lawyer-client relationships often involve just the giving of advice. It would be odd for a doctor-client relationship to not include examination and treatment.

This is a totally valid point, but it does make me wonder: why don’t psychotherapists behave in a similar manner to lawyers with this type of disclaimer? Maybe because it’s not a therapy session unless you sit down for an hour in a private office?

People get self-aware of the dangers related to their profession. We get pretty crazy about data leak, when nobody else really cares. I'm pretty sure the psychotherapist you just talked to at a dinner party has one or two diagnostics on your mental health and has an opinion on your relation with your parents, and lawyers always think about what can get you sued. So they get really careful when there's a legal risk for them.

The rules for establishing attorney-client relationships are different than the rules for establishing a patient-doctor relationship.

And, the duties and responsibilities of a lawyer to their client are different than for doctors.

They could be made the same but that would require new/more laws.