In the US in particular there is not much evidence people are engaged in their local community or know anything about local politics. In many countries the turnout for local elections is far lower than the turnout for national elections. In the US turnout in local elections have been consistently low in comparison with national elections.
Local government is just as likely to be taken over by wealthy and out of touch elites as the central government is. Small communities often contain a large number of voters who hold extremist views and who put pressure on local government. As a result, local government often endorses strange, extreme, and unhelpful laws which increases voter frustration with democracy.
More local government does not necessarily create more democratic engagement. Local government is just as likely to be out of touch, elitist, or held to ransom by extremism as the national government. Local elections typically have low voter turnout.