More resistance is less load??

there might be measurements that suggest that there were other benefits that made foregoing better measurements at the amplifier worth it.

That measurement is power, which equates to sound pressure. Otherwise there is no real advantage to a low impedance load.

One thing I forgot to mention is how much more important the speaker cable becomes when driving a lower impedance. Into 4 ohms the speaker cable is critical and differences are easily heard between them as a result. Conversely, at 16 ohms the speaker cable is far less important and longer runs can be made with less deleterious effects.

Into 4 ohms, the speaker cable can easily degrade the damping performance of the amplifier. So if your speaker requires a higher damping factor (+20:1) then it will be important to keep the cable as short as possible to minimize its effects. I've seen this have dramatic effects on the resulting bass impact!

AFAIK long time ago all speakers had higher impedance, mostly 16 ohm but some even 32 ohm.  

Linearity would be much better with underhung motors (coil within a gap) instead of commonly used overhang motor design (gap within a coil). Only few manufacturers use more expensive underhung (larger magnet) design.  One of them is Acoustic Zen.

A long time ago amplifiers had a great deal of trouble dealing with low impedances and high power. With the advent of reliable ss amplification that can double down, speaker designers were free from those constraints to advance other aspects of speaker design.

A long time ago amplifiers had a great deal of trouble dealing with low impedances and high power.

I’m not sure why. Output transformer can be designed for any load. Perhaps higher impedance speakers had less distortion? Perhaps it was difficult for high power SS amps to deliver high output voltages?