Low-sensitivity speakers — What's special about them?

It’s not just about bass, one needs to consider the source the root causal reason for higher output.

one form of higher output is achieved with a mechanical device to focus energy - imo at cost to fidelity. Horns are not everyone cup of tea. Since to appear focused on dynamic drivers, I will comment more about those..

for dynamic driver speakers, non pistonic motion creates higher output thru constructive and destructive interference. Check out the Utube video on the comparison of two 5” midrange, for a dramatic and easy to understand visual representation of in and out of phase behavior. That video is linked on the Vandersteen website. For a non pistonic driver ( most of them frankly ) A great deal of output is just in and out of phase trash. When a pistonic cone assy is fitted to the driver with equal mass, output drops. The bottom line is trash counts in the efficiency measures. Another reason to listen and not get too wrapped up in less than critical specification. Pay attention to impulse response tho!

IMO a fantastic speaker for you would be Vandersteen VLR signature on Sound Anchor stands with a Vandersteen Model 3 subwoofer with 11 bands of analog EQ for perfect bass at the listening position and a built in amp that takes load off your main amp yet preserves transfer function of the main amp

I've not bought any power yet. Thanks for the replies. I understand the technical trade offs better, now. If one had the bass covered by a subwoofer, it seems there’s no positive, specifiable, aesthetic reason to prefer low sensitivity speakers. I think that captured every remark so far, no?

+1 tomic601.  I have installed a  pair of Vandersteen Model 3 Subwoofers.  They are sublime.

What it comes down to is... really good mids with any type of top end extension without cone break up is hard to find in true high sensitivity speakers.  It has already been mentioned about bass.... The bigger the magnet/motor structure of a woofer, the more sensitivity and the more mass it needs to produce low fs/Qts.... these are attributes that lead to deep bass.  As you as you ad mass fs goes down and qts goes up,  but the trade off is that sensitivity goes down.  
Its not a perfect world.  I try to find the sum of parts as a whole to start the design process. Not being able to find any single part can kill an entire speaker project.  
Alot of people really like sealed box speakers for bass, I am one of them, but woofers that work well in a sealed box need a qts of a minimum of .4 and preferably .5 or even a bit higher.... Look at spec's on high sensitivity woofers,  you'll see .2 to .35.  This is just too low to produce bass in a sealed box system,  Although .35 can produce very satisfying bass in a ported or vented design.  You also have to consider that most good designers prefer to keep the crossover out of the vocal range,  so again,  it requires drivers with a fair amount of extension on the top end or bottom to pair with other drivers. 
There are plenty of excellent parts to design high quality low to medium sensitivity 2 or 3 way systems with great results.