Thermal Distortion your loudspeaker most likely suffers from it. But do you care?

It is usually referred to as thermal compression—as music gets louder (more current flowing), the heating of the voice coil means that any increase in the signal level does not result in a proportionate increase in sound level because the heated wiring resists the current flow. This is the principle reason why high efficiency speakers tend to be more dynamic—far less thermal compression.

Crossover components most certainly can get hot enough for thermal compression to be an issue.  A friend of mine who repairs gear showed me a couple of inductors he took out of a pair of speakers that where played at a really high volume level.  Remarkably, the drivers were not blown, but the plastic formers for the inductors completely melted--what was left was a spool of wire sitting in a pool of plastic.

ditusa,

Thank you for the interesting paper you attached to one of your postings.  I just got around to reading it and it is very interesting. Not only does heat affect the voice coil, to the extent the heat gets into the magnetic structure, flux is affected which further adds to thermal compression.  I also did not consider that changes in Thiele-Small parameters also add to compression.  Finally, I might add that although the paper does not mention this, heating of the components in the crossover will add to compression.  

I have woofers and midrange compression drivers that utilize alnico magnets.  I don't plan on abusing these drivers to the point where de-magnetification occurs.   A local dealer who had an alnico magnet driver with weak output had the magnet recharged, it did not cost that much to have this done.  I have no idea about the particular effect of the type of magnet employed in a driver, as far as the sound is concerned, except that many of the drivers I like happen to have alnico magnets (and pleated paper surrounds, and other old school design features).

The interesting thing about Alnico magnets and compression is that some theorize that the particular sound of Alnico magnet speakers is that they are actually subject to more compression than other magnet types because flux density is lower under dynamic conditions when the voice coil is excited. 

As Atmasphere described, cost was a big driver to higher power and lower efficiency.  But, it was also partly a result of the success of stereo.  When it was just one box, it wasn't quite so bad that the box was big in size.  But, when stereo came along, there was a big push toward making smaller speakers.  Smaller size meant lower efficiency, but, that tradeoff was now possible because the transistor made it possible to get more power relatively cheaply.