Is there any advantage to lower efficiency speakers? 87 or below?

Thanks everyone!  These are really good explanations. 

Low efgicience speakers can make your amp woek put to stay strong. Actually, most such speakers gave power sucking, elaborate crossovers to get a flat frequency response. Newer designs use better parts and of course designs. 

Everyone is sort of missing the real cause & effect..... It's not impossible to make drivers and speaker systems that are 97dB efficiency, but they will have far from flat frequency response or tight transient response. (though they can still sound musical).  Very light drivers with large magnets, and/or horn loading will have peaks & valleys in their frequency response due to undamped resonances.  In a magical world, you would raise those dips UP to meet the peaks, and have a high sensitivity speaker with a smooth response.  But that's not reality.  All we humans can do is damp those peaks down by adding mass, stiffness, damping, whatever, etc.  By the time you are done tapping down all those nasty peaks, you are down to 90, 88, maybe 86 dB.... all depending on about a million variables and design choices.  Then you put it out into the world, and see if people like what you did.  Nobody sets out to make a low sensitivity speaker as a goal.  

From Wikipedia:

"The acoustic-suspension woofer uses the elastic cushion of air within a sealed enclosure to provide the restoring force for the woofer diaphragm. The cushion of air acts like a spring or rubber band. Because the air in the cabinet serves to control the woofer's excursion, the physical stiffness of the driver can be reduced.

Unlike the stiff physical suspension built into the driver of conventional speakers, the trapped air inside the sealed-loudspeaker enclosure provides a more linear restoring force for the woofer's diaphragm, enabling it to oscillate a greater distance (excursion) in a linear fashion. This is a requirement for clean and loud reproduction of deep bass by drivers with relatively small cones....

Acoustic suspension woofers were once very popular in hi-fi systems due to their low distortion. Compared to bass reflex cabinets, acoustic suspension has a flatter frequency response and slower rolloff below their resonant frequency. Bass reflex cabinets are generally more efficient, however, and the use of a vent or port in the cabinet provides improved low-frequency response."

I don't guess there are too many fans of acoustic suspension speakers anymore, but I still have and love my Boston Acoustics T-830s from the 1990s. They claim 90 db efficiency; but they take more amp power to drive than my big 90 db bass reflex Cantons with 2 more woofers.