What is the quantifiable benefit of compressionless brake housing?
It's about distance, not force. Coil housing is not at all impaired in its ability to transmit force once any distance between its coils has been taken up (so no to your second question.) On any rim brake that doesn't have egregious bends, the practical difference between compressionless and coil housing is marginal. It's a little stiffer and more responsive feeling, but the advantages of it are small and possibly outweighed by the increased fragility, installation hassle, and/or expense of compressionless. On a mechanical disc, or a rim brake system that forces egregious bends in the housing, it's a different story.
Total pad gap on a V-brake or dual pivot caliper is around 5mm. On a mechanical disc it's 0.8-1mm. Yet the lever throw powering both is the same; the needs of a brake lever designed for a human hand doesn't change between the two. This demonstrates that in terms of lever movement to pad movement, mechanical disc brakes run at about a 5 times greater leverage ratio, or mechanical advantage. You have a great big lever throw producing a very small amount of movement. That's how disc brakes are powerful despite a rotor being such a smaller circle than a rim. Mechanical discs can have problems with being difficult to set up in a way where the rider doesn't run out of lever travel, and since compressionless helps conserve lever movement by eliminating housing compression, it is good to use in this role and is often one of the main ways of helping out a bike that is having issues with the levers bottoming. This is often most pronounced on long continuous rear brake housing runs, which most disc bikes have.
The effect of coil housing creating wasted lever movement becomes much more pronounced whenever there are tight bends in the housing path, which will cause the gaps between the coils to open up and need to be closed again by the braking force. The helical nature of the individual strand path in braided compressionless brake housing mitigates this effect almost entirely in most cases on bikes. The same effect can sometimes be used to create good brake feel on bikes with brake routing that forces awkward bends.
It is worth pointing out that compressionless brake housing does have a dark side compared to coil. Coil housing, being made of thick steel, is a very robust design that is much more able to shake off or only be incrementally affected by damage, abrasion, kinks, and material degradation. Compressionless brake housing is something of a glass cannon in comparison; it's a bunch of steel wires that fundamentally don't want to stay together and resist the forces they're being put under, but are able to do so because of the standout properties of the layer of kevlar fabric that constrains them. The system is also wholly reliant on the right special ferrules being used to keep wires from pulling through. Compressionless brake housing is safe, more than reliable enough for bikes that are reasonably maintained, and not prone to failing suddenly when it does fail, but it is less age- and abuse-resistant than coil.
EDIT: As ojs pointed out in the comments, I had the part about the effect of compression being amplified 5x wrong, which I initially wrote. I've edited this answer to be something I can stand by, but see that it was likely accepted on the basis of incorrect reasoning, so I'm open to it being taken down or un-accepted as the answer, neither of which I can do.