Wording of your question aside..... from a general standpoint politicians have been expressing values and engaging in cultural appreciation for as long as there have been governments. Whether that's wishing everyone a happy holiday, participating in a parade, speaking at a Veteran's Day event, visiting a school, planting a tree on Arbor Day, or whatever else.

But if you need a more practical reason that aligns with your personal view of a mayor's job, then the answer is already in your examples:

> keep the city safe

> I am happy to hear your thoughts.

Your reasoning seems to contradict itself since you hinge your definition on the idea of lawful/unlawful. So on one end you're saying that executions are fine because it's legal to carry them out, but abortion is not because it's "unlawful" in your opinion... despite the actual laws at this time.