Speculative: Higher driving force requires greater current since the magnetic field in a (voice) coil is a function of the current through it. Transistor amplifiers more easily generate large currents at lower voltage and the output impedance is typically very low. High-voltage transistors are typically harder to make with gain and output capability comparable to low-voltage transistors, and they have more limited bandwidth compared to lower-voltage transistors. It is not too difficult to put multiple lower-voltage transistors in parallel to provide more current drive, but stacking them to achieve greater voltage is more difficult and usually less reliable.
Tube amplifiers generate smaller currents at higher (usually much higher) voltage and with high impedance necessitating a transformer (usually) to provide a modicum of impedance matching to the speaker, providing lower output voltage and impedance with higher current. Tubes are usually less efficient since they tend to have lower gain (not always) and require a filament (heater) supply, plus they do not last as long (lower lifetime) compared to transistors.
So from an electronics side, the advent of high-current, lower-voltage transistor (solid-state, SS) amplifiers enabled lower-impedance speakers with greater dynamic range since more current can be provided into lower-impedance loads.
I am not a speaker designer so can only guess about the speakers themselves. I would guess lower-impedance drivers can handle more power with larger wires and the higher current handling allows longer-throw voice coils for greater output. Lowering crossover impedances (which plays into overall speaker impedance) provides greater flexibility in design and potentially less loss in the crossovers themselves (larger wire for lower resistance in the lower-value coils so less loss). It should also extend the bandwidth on the upper (higher) side but I suspect that is negligible.
I am not sure about efficiency; IME the lower efficiency is more a function of cabinet size and design trades than impedance but again I am not a speaker designer. Specifically, the trade to extend the bass response using a smaller (e.g. bookshelf-size 5"~6") woofer, which in turn requires speakers to "throw away" midrange and treble power by attenuating the mid/high frequencies to match levels with the woofer, which has a lower output. Especially when a small woofer is pushed lower in frequency in a small cabinet.
Edit: Others above already covered all this more concisely whilst I was composing my post (price of multiplexing and trying to stay in touch with a meeting at work
).