Is an analogue audio signal DC or AC?

The speaker perspective is a good one. You are correct that the alternating current moves the cone in and out. An AC signal with a DC component would also move the cone in and out, but the DC portion would permanently move the cone a bit in one direction, making a new zero point, as it were. As you might imagine, this would affect the sound quality.

DC components can cause other problems. Some uses of scrambling in transmitting a digital signal over radio waves are there to remove DC components. There’s no such thing as a DC offset of a radio wave, but the DC component might appear at the receiver or transmitter prior to sending or receiving the radio waves, so the scrambling function attempts to remove significant DC offsets for the amplifiers before the digital signal is recovered (at which point the DC offset is no longer a concern).

I quote a patent to explain this:

I didn’t read the whole patent but this point is interesting to think about.