Here's what others have dug up.
http://www.ft86club.com/forums/showthread.php?t=8267
tl;dr due to the high compression direct injection nature of the FA20 it requires a specific uncommon plug design to operate well.
NGK has some good info on why different plugs matter and the tl;dr there is that different combustion environments need a different kind of spark to operate at the way it was intended to.
https://www.ngksparkplugs.com/about-...rk-plug-basics
Some conclusions you can draw from that: spark plugs are cheap because of economies of scale, there are literally hundreds of millions of spark plugs manufactured every year and I'd bet most of them fall into a few categories. When you make tens of millions of widgets per year you can get production costs very low, but for the FA20/BRZ/FRS/86 they're only making maybe a few hundred thousand per year.
Take the spark plug in a Toyota Camry, instead of making 50 million of those every year you only make 5 million. It doesn't cost any less to setup the factory and maintain the machinery but you are all of a sudden selling 1/10th of before, therefore prices must go up nearly 10-fold to maintain profitability.
And that's how what "should be a $2 spark plug" is now a "$20 spark plug"
(except now rare metals increase base cost but don't necessarily translate into lost profit margin based on economies of scale so we're comparing a $20 plug to a $8 plug)
Why do I think this is true at all? Because if there was any other engine using this spark plug it would have been known years ago and yet every parts website lists it as the only option for this car and nobody else uses it. If you can find something that does then I'll re-evaluate my hypothesis.