I don't find it too much of a stretch to assume that just because we've only seen Kyber crystals make blue, green, and yellow sabers, that they can't make any other colors. I think there is a bit of the Force reading the characters and that is what gives the saber it's color. Obviously the Kyber (just like everything else in the Force) initially resists Sith, hence the need to force it to their will (just like they do with the Force), which explains the Red just fine. We've only seen one canon Purple saber, so maybe the Force (and by extension the Kyber) senses each character, and then the color comes for what they are most aligned with. Most Jedi are relatively simple, hence the Blue and Green, but someone like Mace Windu (who from what I understand is a more aggressive person to begin with) the Force would give him a purple blade. Someone like Vizla (who is a MANDOLORIAN) would have a far higher aggression rating than even Mace, so the Force would give him a Black blade. That is what I think (if that makes any sense).
I also don't think that the only way to get a Silver blade is to cleanse a Sith crystal. And my reason for thinking this is because of Master Sinube also has a Silver blade. Does this mean that he did not cleanse a crystal? Not necessarily, but seeing as the Sith have been gone for nearly (or maybe over) 1000 years, and the average lifespan of a Cosian (Sinube's species) is about 200 years, I find it highly unlikely. Anyways, just some thoughts.
I forgot about the Clone Wars episode specifically where the one older Jedi (can't remember the name, but he is instructing a youngling lightsaber class when *SPOILER* Anakin and Barriss have their wicked awesome duel), he inexplicably had a white saber in that scene if I recall and strangely enough I think in a different season he had a green one. Then of course you've got the Temple Guards with their special yellow saber staffs. It's been a bit since I watched the series in its entirety but wow, it sure confused the issue of blade color. And that's excluding the Darksaber completely.
Hey Sani, Samuel L. Jackson is totally to blame for all of it. Lucas told him that "good guys get blue and green" but he just HAD to have that purple.
That is who I'm talking about, and earlier he had a light blue (still could've been considered Silver).