To clarify, local (i.e., municipal) police does exist (generally in towns and cities with more than 5,000 citizens), and is usually called guardia urbana, policía local, or policía municipal. These are who you'd call for a noise complaint.

There's also, as I said, the policía nacional and the guardia civil, both operating in the whole country.

And some autonomías (states, if Spain was federal...ish, which it sort of kind of is somewhat supposed to be, in theory, but effectively isn't, in practice) also have their own police force (which doesn't mean the others won't also operate there, of course).

It's a complicated country, mostly because it's really several, held together with duct tape and, occasionally, barbed wire.

Is there large public demand to disband them?