Somewhat relevant to the conversation: Pablo recently did
an interview with Collider's Jedi Council show and again clarified the mechanics of the process. What's most interesting to me however is that he says all of this came out of the development of that youngling arc from TCW (which seems like it could have been a backdoor pilot for a new show) and the lore came straight from Lucas himself. So it's not something they just made up recently, this is how the franchise creator thought it should work.
Unfortunately, it wasn't the theory that circulated around in things like "Star Wars Insider" or "The Visual Guides." So, it may not be new, but it wasn't well known, if that makes sense.
Claiming and dominating one's own crystal is probably as much of a trial or rite of passage for Sith as it is for a Jedi to hear the crystal's call and forge the bond. Sure, the respective masters could just give them out but then where's the lesson/challenge in that?
Now yes technically, as far as we know Kylo and Snok aren't Sith, but they certainly seem to be emulating at least some of their ways.
Well, if the Sith master is setting up the trials to find the crystals, then they would have more control. But, I see your larger point that the trial would be the showcase their power to their Sith Master, which is keeping with the Sith quest for more power (insert joke here. There are several).
As for Kylo and Snoke, Snoke appears to utilizing Kyber crystals far more than the Empire ever did, and is more open about his Dark Side users. So, while they are Dark Side users, Snoke clearly is finding ways to expand his power base with his Knights of Ren. So, there might be other Dark Side users, influences or uses for the Kyber crystals than the Empire was willing to do.
As for the rarity: well why is anything rare? It's just at the low end of a probability curve. Exactly why so few turn purple or white is something they haven't gotten into yet. Mostly because so far it hasn't been massively relevant to a story yet. So patience young padawan.
I'll attempt to be patient, but, as I said, the idea that the color changes in response to the Force bonding of the Jedi or dominating of the Sith is one that indicates that other colors could occur, but are rare because...?
Also, it asks the questions if Kyber crystals and the like can be used for other purposes without the assistance of the Force? In Legends, there were lightfoils, which were used by nobles on a planet for dueling. Not full lightsabers, but a similar idea.
"And whatever you do, don't just snag one of the hundreds of thousands of sabers that were around about 50 years ago, give or take. Because, you know, they were like... incinerated or something. Because why would the Emperor have wanted to stockpile all those rare and precious crystals from them? Yeah, screw that, just take this shitty one you broke and deal with it."
I think it's more a matter of, "You done screwed up, son."
Lore written by a guy who's writing is so bad that the moment he sold his franchise, the new buyers were all like "yeah, no thanks buddy, your new ideas are shit." Oh, and who thought people were clamoring for a trilogy about trade politics and a woman falling in love with a toddler. Don't forget to add those bits in.
To be fair to GL, Anakin was originally older but he didn't buy that separating from his mom would be that big of deal. Rather than rewriting Anakin's arc in TPM, he changed his age. So, unfortunately implications resulted.
But, I've always enjoyed GL's view on Star Wars lore, so the idea the the color changing crystal due to bonding is something that was previously considered is at least interesting to me.