Huh. No? There are people elected to work at say EU level, national (country) level, regional level and municipal level. The mix can be different parties and in many places the municipal councils and mayors don't even have to be in a major political party.

You have it similar in US. I bet a mayor can build sewers, collect garbage and build a lot of roads without asking the governor or president.

Or did you conflate government with public sector?