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