Different levels of government (federal, state, local) have different duties in their task of serving the US citizens. They are organized in such a way that one should not interfere in the competencies of the others.
Local government are in charge of providing services such as education, police, fire department, green areas and parks, healthcare facilities, highways, housing services, and many others.
On the other hand, driving licenses are issued by the state, as the same rules apply to all its citizens.