The analog computer is a quantum system (of atoms for example), and your argument rests in that the complexity of simulating a system of atoms is not high and that nature (i.e. the "analog computer") isn't performing something better from a complexity standpoint.

While I agree that there are pretty efficient algorithms to simulate systems of atoms behaving like Newtonian bodies (like molecular dynamics) it quickly falls apart when you need to include more "quantum like" effects.

The digital quantum computer is itself built out of atoms, so if you could simulate an analog computer (which derives its properties from QM) efficiently, you could then also simulate the digital quantum computer efficiently.

I guess it's a question of semantics - like what properties of nature are an "analog computer" allowed to tap. My point is, I think, that you kind of downplay the capabilities of what an analog computer is capable of by saying it's "just" an analog computer. But any small molecule whizzing around is in some sense a very difficult to simulate analog computer from another point of view.