No, nobody imagined adding a speaker without wire. I imagined adding a speaker and figured the OP would know wire was needed.

buzz,
that's a neat picture to paint, that it can't look down the line! True. All it can do is see the impedance right at its output terminals, and that includes the speaker and the wire along the way. In both directions... but it can't tell how much wire there is; it can only see the effect of the load.

It's not as simple as "the impedance varies wildly."  The impedance does not vary at all, actually.  It's different at different frequencies, but that's not something varying, that's something looking different from different points of view. But I think you know all this: The impedance is what it is at each frequency, so if you measure the impedance and don't notice that you're changing frequencies, you'll think the impedance is changing. The impedance at any one frequency is the same all the time unless you squeeze the wires or add or subtract capacitors or inductors without noticing. (I say without noticing because you will expect the impedance to change if you know caps and coils are being changed.)