I basically get what you're saying, but...I dunno. The idea of a world of unconstrained shapeshifters just doesn't strike me as a very interesting possibility; a lot of what makes "Iridescent Sun" interesting is the wide variety of changes people have gone through and their own individual stories as they try to adjust to what they've become. Maybe some of them really would be happier being their old selves, maybe some wouldn't, but the idea of freely switching just seems kind of boring by way of being pretty noncommittal. And I do think (as suggested in the chapter) that it would kinda impair people's attempts to forge a coherent new self-identity, since any such "self" would have to encompass two (likely wildly) disparate existences.
I totally get what you're saying about keeping things from being authoritarian, but that's the exact reason Jon is suggesting leaving it up to the stone; capricious as it can be, it's the closest thing to a truly neutral mediator they're ever going to find, when used carefully. It's less a case of her telling other people what to be, and more her doing everything in her power not to put herself in that position, while still resolving the issue in a conclusive manner.