I remember reading years ago about prohibiting politicians from practicing if they proposed too many laws that we found to be in conflict with the constitution. I believe ancient Greece had something like this but cannot find anything about it anymore.

It is arguable whether this impacts freedom of speech, and it would be argued differently in different jurisdictions.

It absolutely does - when this same law was implemented in Germany as a national law it was struck down by the constitutional court.

Germany is not all jurisdictions, that is the point.