It's unlikely that state bar rules can be challenged due to the commerce clause. I'm assuming you mean the dormant commerce clause because the ICC would clearly favor more regulation, but by the Feds, not the states.I seem to remember a case from Con Law in the '50s or '60s when someone challenged the bar admission rules under the privileges and immunities clause, probably something about requiring that a state allow non-residents to take their bar exam. But I don't see how the ICC or the dormant commerce clause could be used to challenge state bar rules when it's long established that each state sets its own bar, literally, including the admissions standards (and doesn't discriminate against the privileges and immunities clause, although I could see how you could try to make that argument, likely unsuccessfully).