All governments get their power from the people who they serve. As soon as they do not serve the interests of the people the represent they should be dissolved. Local government gets its power from the local people and no one else.

Most obviously their form and powers vary based on the state.

Several hundred years of court cases make there limits clear. Local governments regularly get overridden on all kinds of things.

Local governments are also completely dependent on outside help for all kinds of things. It’s common for them to even lack local police forces let alone a court system. Outliers like major cities seem extremely powerful, but for the most part they have similar powers to HOA’s.

PS: As to getting authority from the governed… Some let people outside the area vote, and a few that give corporations a say.

I know it's out of fashion, but the Tenth Amendment appears to say otherwise.

The 10th makes it clear the constitution gives the federal government specific powers which means those specified powers aren’t available to the states or local governments.

The first draft is a little easier to understand: “Each state retains its sovereignty, freedom, and independence, and every power, jurisdiction, and right, which is not by this Confederation expressly delegated to the United States, in Congress assembled.” (Which is not) can be flipped to the front so -> “Those powers given to the United States are its alone, all other powers not specifically listed are retained by the States.”

Both versions makes it clear states are losing some power, but they are given a little spin to make it less obvious.