@Observer: as I understand the song, its target is exactly what you say, i.e. it argues for a change in the political system, so that the persons mentioned can be "fired".

(Your point 2. may be misunderstood by those unfamiliar with the British system; it should run: "Like the UK, the US do not allow a binding single nation-wide vote.")

Songs are about emotions, which often tend to be paradoxical. The call for "more democracy" may argue for smaller or larger political units, depending on the expected outcome in a particular matter. For example, the (legally non-binding) national referendum you mentioned went against the larger unit (EU) and the smaller units (constituencies as represented in Parliament).

Laws and systems can be changed, and political songs can help sorting out the emotions and arguments. Well, most of them fail, but this one is not among the worst, in my opinion.