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A d12 is so good for creating rolls that are isomorphic to weirdo d6-with-exception situations.
What I mean is that if I want a one-in-six chance of one thing, but otherwise a 50/50 chance, a d12 is great. Or, if I want a one-in-six chance and in that case a 50/50 chance, a d12 is also great.
Because a d6, if you remove one of the six outcomes and make that special, that leaves five sides and five isn’t very divisible with two or with anything. But with d12 if you remove two sides you get ten left and that’s great for splitting into two.
For example, initiative in RC is d6 vs d6, on a tie they go at the same time. Those two d6:es can be replaced by a single d12: 8+ party goes first, 6 or 7 both sides at the same time, or five or lower the pretties goes first.
Yeah, yeah, I know that isomorphic outcomes to RAW is a huge hobgoblin for me when I make house rules. Same when I was making houserules for 5e. I made plenty of house rules to simplify the math but that gives more or less the same results. I’m not convinced that a one-in-six chance of a tie is especially sacred or necessary. But, I see a rule, I wanna simplify it, either the math behind it or the UX in front of it. In this case more the latter (replacing two rolls, and talking & comparing that roll, with a single roll) than the former (a d12 table with two separate thresholds is fiddlier & harder to remember than a simple “highest goes first”).
Or, I’ve been using a d12 for random NPC gender for years: odd = dude, even = chick, except eleven = gender unknown (whether it’s deliberately concealed or just hard to tell, you don’t know, and maybe there’ll be a reroll later if this NPC ends up sticking around) and 12 = enby. (Although most of the time I don't roll on this because wallpaper saliency rule 🤷🏻‍♀️ i.e. this stuff feels like it's OK to improvise..) That wasn’t me trying to be isomorphic to anything, it’s just something I came up with. A one in six chance for the two special cases felt lagom compared to the one-in-ten if I had used a d20 or a one-in-five if I had used a d10.
I guess the principle to have the special case be * of the sides, so that either the special case and/or the non-special case can then be split into two equally probable outcomes is applicable to all dice with an even amount of sides, and the only thing that makes the d12 special is the portability from rules written for a d6.