Why don't we elect many specialised governments instead of just one?

Lots of countries do elect several governments with different responsibilities. including the country where I currently live. One runs kindergartens and hospitals, another runs the school system and the police, a third runs customs.

I think the answer to the question is that the split isn't simple. 60% of laws enacted require cooperation between different levels here, and that's after a recent reform to split the responsibilities more cleanly.