What makes a speaker sound great at low volume?

Plenty of speakers with low 90's sensitivity sound dreamy at low volume. And they don't force you to use the absolute quietest electronics available. 

My rec room speakers are a pair of vintage DCM TimeWindow 3's.  I set the volume on my McIntosh 31V A/V control center to an acceptable level and then use the 31V's EQ and McIntosh MC2600 power amp gain controls to tweak the sound.  This system is all analog.

In my music room, I have a NAD M12 and NAD M22 v2 pushing a pair of Tannoy dc8ti speakers.  This system is all digital, except for my Techniques SL 1600 MK II turntable.  I use the M12's volume control, which works OK - but , the treble and bass controls are no match for a good EQ like the 31V

I don't know if particular design attributes contribute to, or detract from, low level listening.  But, as a general observation, the best sounding systems at low volume tend to be high efficiency designs, particularly horn-based systems.  It may seem odd, but, those massive horn systems play better at low volume than at high volume (this might explain why so many Japanese audiophiles are attracted to horns even if they have neighbors that are very close by).

In part, high efficiency allows for the use of low-powered amps.  Low-powered amps, particularly tube amps, sound very lively when played at modest levels, while high-powered stuff tends to sound dead at low volume.

chayro: Love your first sentence ...

OP: I don't know if you're considering vintage speakers as well, to solve your low-level, listening issue, but I have a pair of Kef R107's, and they produce a wonderful sound-stage no matter where you are in the room. They are supplied with a small EQ adjuster that is electronically, part of the crossover. At low volumes I just boost the Contour adjustment dial. (This is the only time I touch the contour dial). This seems to add what's required to cover all the necessary frequencies, and the music sounds great.
Most people seem to like the 107s, but some just don't. They're a little different.
Anyway, just my two cents ...

IME, active, near field, studio monitors are probably the best bet.  Get the x-over ahead of the power amps and you’re most of the way home.  The best examples are quite expensive, but even many of the modestly priced units are very good at lower SPLs