No, it wasn't Spotify, it was Muzak. Muzak went bankrupt in 2009, but for decades, they provided piped-in music for stores and elevators, distributed over phone lines.

The Teleharmonium was one of those painful things people built before power amplifiers. It had a big AC generator for each audio note. That's why the thing was so huge. They had no way to amplify, so they had to generate each note with a big enough generator to drive all the speakers in the system. At any given time, only a few notes were active, but all the generators were turning. This wasn't a promising line of development.

Tone generation using rotating machinery did make a comeback in Hammond organs of the late 1930s, which had a tone wheel for each note. This system had amplifiers, so the tone wheels were small. Hammond organs were noted for being absolutely in tune; all the wheels were on the same shaft, and driven by a synchronous motor, so they had to stay in sync. The Hammond was a good organ, and emulations of the original models are still sold.

There's a whole history of early amplifiers. Edison even built a steam-powered public address system, the "Steam Shout". This was a diaphragm connected to a needle valve in a steam line. It was apparently a flop. However, now that we understand how to build fluidic amplifiers, it might be worth revisiting that idea. It would be a good accessory for a steam calliope.

Other early attempts at an amp include Edison's "chalk telephone", the electromotograph. It turns out that you can build a clutch by running a current between a rotating damp chalk cylinder and a wiper. As the current changes, so does the friction. This is due to the Johnsen-Rahbek effect, which is a semiconductor phenomenon and wasn't understood until the 1950s, but was used before it was understood. Once the theory was figured out, it was clearer what materials to try. Silicon carbide was much better than wet chalk, and this effect was used in IBM line printer clutches. Edison used this to make a "loud-speaking telephone". It would be worth trying that idea with a silicon carbide disk or drum, and perhaps build a steampunk amp.

Other rotating-machinery amps include Ward-Leonard drives and amplidynes. These work on the principle that modulating the field current of a generator affects the output. This only works at frequencies well below the output frequency of the generator, but there are ways to build high-frequency generators, such as Alexanderson alternators. Realistically, though, you probably wouldn't be able to drive anything faster than a subwoofer with reasonably sized rotating machinery of this type.

There are magnetic amplifiers. These work by saturating the core of a transformer with a DC signal to stop it from passing AC.[1] These work quite well as lamp dimmers and motor controllers, but they're mediocre audio amplifiers. You need a source of AC at some ultrasonic frequency to make this work for audio.

In 1906, Lee DeForest developed the "Audion", the first three-element vacuum tube. That was the beginning of electronic amplification, and the beginning of the end for all those clunky alternatives.

[1] http://sparkbangbuzz.com/mag-audio-amp/mag-audio-amp.htm