...1. If using a water-based quenchant, brine is less likely to result in distortion/cracking than plain water.
Theoretically, yes, but it doesn't always work out that way for us due to the size and shape of our steel.
...2. Water-based quenchants are fine for, say, hammers and anvil faces, etc., but not so ideal for items with edges due to reasons you mentioned.
Water is cleaner, easier and cheaper than almost anything and yet almost all industry has abandoned it for expensive, messy, and more hazardous mediums. BUt in the long run it is cheaper to keep all your parts instead of sacrificing a percentage to distortion and cracking. Typically industry has handled this by developing the alloy around the problem and not the quench medium, first they developed oil hardening steels and the "W" and 10xx series were phased out, now, tiring of the liquid hassle altogether they are opting for air hardening alloys and steels like O-1 are being replaced. Even the very skilled guys doing Japanese style blades in water will admit that they lose as much as 1/3 of their blades to the perils of water, I personally can't make a living doing that, and I also have tools to allow me to see inside the steel that "appears" to have survived the water only see the micro-defects from it.
...3. Concerning the example of Japanese swords, my belief until now was that the differential hardening process through use of clay coating was what created the sori (curvature). Inferring from above, it is not only the insulating properties of the clay, but just as importantly (maybe even more so) the quench medium being used...
Absolutely, quench such a blade in oil and it starts to curve in the opposite direction, reverse sori is a big aggravation for many smiths when they first make the transition to oils for such blades.
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I believe the primary goal was to have a hard edge with a tough (soft) spine, and the curvature was simply a byproduct of the process being used.
Now, the curvature is desired for aesthetic reasons, not merely a byproduct of obtaining function. Is this why the swordsmiths continue to water quench, or is it merely "clinging to tradition"?
Several things going on here, different parts of the tamahagane bloom with different carbon levels were often combined in the blade to overcome brittleness as well as the differential hardening. The curvature may or may not have been unintentional at some point in antiquity, but it is much less aesthetic than essential to function on a single edged blade like the katana, the cutting action is greatly enhanced in the style of cut with that type of sword.
Now as for tradition or necessity of water, here comes the one crucial point that most people overlook when thinking of water quenching because of tradition. Ancient steels, like bloomery steel and tamahagane had no intentional alloying whatsoever, they were simple iron carbon systems, and thus they were
incredibly shallow hardening even when compared to W1 or 1095. W1 or 1095 has extra things in it, whether listed or not, and would not survive many of the same treatments that a piece of bloomery steel could. The downside to this is that those simple iron-carbon steels did not have the same impact toughness that modern steels do (trust me they don't, I work with them a lot these days) and so all you could do is adjust the hardness levels in order to gain toughness. Thus you went with a lower Rockwell all around, differentially hardened, or welded together different hardness levels. Making swrods today you can quench an alloy in oil and temper it back to 58 HRC and get 3 times the toughness of those old steels at a much higher hardness. So the tradition is not so much in the water, but in using the ancient steels.