Why are loudspeakers manufactured in various impedance values?
You use different speakers in different systems and even different serial and parallel configurations; that's one of the reasons there are different impedance values. 8 Ohm speakers are the standard for home, while 4 ohm are usually found in car audio systems. 


  If a lower impedance loudspeaker generally has better dynamic range
  and can achieve louder volumes, why do we still see 6, 8 or even 16
  ohm speakers? Shouldn't we be "progressing" toward more efficient
  speakers with lower impedance?


While yes, the benefit of 4 ohm speakers is that the increased current means they have a wider dynamic range, they will be harder on the amplifier (if the amp is made for 8 ohm) and at higher volumes they will have larger THD (total harmonic distortion.) Essentially the output voltage will be unstable during high power application as the Amp will struggle to supply enough current to drive the load.

Using a 4 ohm speaker on a generic home amplifier that is made for an 8 ohm speaker will draw twice as much power and can cause the amplifier to go into protect mode or even overheat and break. 


  why do we still see 6, 8 or even 16 ohm speakers?


Different serial and parallel configurations are used to change the load on an amplifier. For example, you can have two 4 ohm speakers in series so that the load will be 8 ohms. Or (common in custom car systems,) you may have two 4 ohm speakers connected in parallel so the load on the amplifier is only 2 ohms, thus doubling the current.

Or in this case, four 8 ohm speakers are connected in series parallel so that the total impedance is only 8 ohms.




  Are higher impedance speakers merely a product of
  backward-compatibility?


No they have their place, from allowing different speaker configurations, or less wear and tear on amplifiers to improved sound quality.

Using speaker with higher than minimum impedance may improve quality as the Amp will generate more stable voltage and current. Hence the THD will remain lower at higher impedance while the maximum power output by the Amp will be reduced due to higher load impedance.


  Loudspeakers have impedances of 8 ohms, 6 ohms or 4 ohms (those are "nominal"  or approximate values, because the impedance of a
  speaker changes all the time with the different frequencies of music


They are also referred to as at rest values, and if you connect a ohm meter to the speaker it should read 4 or 8 etc. ohms. Then if you gently move the speaker that reading will change. If you measure a speaker and it shows a different value than what it is supposed to then it may be defective of blown or at least slightly damaged.