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

This is meant not as a right or wrong thing but more of an observation
 as a recipe for success or consistancy.
It is not that speaker designers deliberately design low sensitivity loudspeakers but in order to seem natural or flat all drivers need to be padded to the one driver that is lowest as mentioned above.
 With cost effective means to look at breakup behavior of cones and domes available today one reason some designers end up with lower sensitivity is that speakers end up that way when using drivers that are breakup free in their passbands or range of operation.
  In most loudspeakers especially high sensitivity ones some of the apparent sensitivity is output from the random ringing of the cones.
 This definitely will smear the music fed to the speaker.
 Low wattage single ended tube amps definitely have a sonic signature and if that is preferred one has no choice.
 But for most of us higher power good sounding amplifiers are available  for reasonable money.
 Best
JohnnyR

Like most things it is a trade off. Lower sensitivity speakers are generally more linear, have greater bandwidth and are generally more accurate (less distortion). It is easy to make a high power amplifier that is extremely accurate (just expensive) it is also easy to make a giant speaker box to get great accurate low end efficiency (again only expensive to build and ship). It is extremely hard to make a light weight diaphragm or cone with a small drive motor and drive it with next to no power and still get anything approaching high fidelity. Just think about it - all of the friction, resonances and other issues of the mechanical cone are relatively much larger compared to the relatively weak but highly accurate drive electrical signal in a high efficiency design.

High end Studios (million $ facilities) have gone gone away from horns for this reason - lower efficiency speakers tend be more accurate and horns tend to have a shouty character due to directivity and non-linear air compression at higher SPL.

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.