I would guess the main reasons balanced connections are not used more widely are due to the cost, the lack of readily-available (and thus cheap) differential drivers, and panel area (XLRs are bigger than RCAs). Also the chicken and egg bit; nobody asks and other components don't have them so why should I?
Balanced, assuming fully differential, circuits offer lower distortion (cancellation of even order terms), higher SNR (3 dB for each doubling of signal level), and greater noise etc. rejection than comparable single-ended circuits, but XLRs cost more and more importantly the circuitry inside is more complex and costly. The vast majority of op-amps have single-ended outputs, though many DAC chips (the actual device inside, not the box) have differential outputs to reduce glitches, lower distortion, and all that jazz.
For me having a balanced output means I can run long lines to a couple of rear subs on a different AC circuit without ground-loop and noise problems but by and large balanced is not needed in consumer installation. That is not to say some would not benefit, of course, and a lot of folk struggling with ground loops likely wish their components had balanced I/O -- if they knew to ask for it. XLRs also offer positive capture and retention which may or may not matter to most. I would guess single-ended is fine for most people so not enough demand.
Great succinct explanation, Don.
Just as reducing Leakage Current with the method of swapping plug orientation, Balanced vs SE can have a big difference in SQ, and you don't even need a long run to notice it. It is a night-and-day difference, so it must be tried.
With my studio monitors, which are active and bi-amped each, I had the opportunity of comparing SE to Balanced on initial setup, and there was such a big difference that I never used the SE in my studio since.
In this respect, some of the high-end gear lags behind the studio gear.
It's a must-try, especially a true, properly Balanced implementation (i.e. without Pin 1 issue - some gear using XLR have this issue so give a distorted perspective of what Balanced should be, which was why Neil Muncy - RIP - was traveling around to show manufacturers and others how to resolve this).
Another thing one could try is Balanced Power, there are caveats to it one needs to be aware of regarding safety.
Another way to reduce Leakage Currents is to use a "disconnected" PSU like the Uptone Audio UltraCap LPS-1 or the Vinnie Rossi Pure-DC-4ever PSU.
There is another more complex form of Leakage Current which is less known but which can only be characterised by the interaction between at least 2 PSUs and their circuits in a chain and aided by the interconnects.
Clean Power and clean grounding is a complex matter, there is a fair chance that people doing default connections aren't getting to hear their gear properly.
Some SQ effects are also rather insidious as some may get used to them after a while. However, a rudimentary AB definitely shows the difference when changing configurations.