Dreamstone, as I understand it, was used both as currency (I can't remember the exact quote) and as a symbol of power (I believe it was Ayla who said that the strongest received it). Going solely by that, I would assume that the prehistoric humans, sensing some sort of natural, magical pull to the Dreamstone, valued it more highly than other materials.
It could be that the Dreamstone nurtured planetary magic, and, perhaps, is contained in a distant descended form inside of Chrono Cross's Elements (I know nothing of geology; please don't kill me), so that would probably be the source of, say, Azala's magic (if we assume it was magic, and not psychic/timewarp power). Heck, this type of stone may even be a sort of cousin to the Sun Stone, which is known to possess natural magic, and thus holds enough magical power of its own to create such artifacts as the Masamune and Schala's Pendant.
My guess is that the Frozen Flame, a splinter of the ridiculously powerful Lavos, serves as a sort of counterbalance to Dreamstone -- they seem to be made of similar magical power, but the Flame is more predisposed to the dark side of things, being basically a piece of Lavos Lint -- and that, given the proper stimulus, the Dreamstone could serve as a medium for conducting the elements. This would also probably have something to do with the fact that the Masamune weakens Magus, with his powers inextricably tied to Lavos, and therefore the Frozen Flame, as its magic would react, dispel, and reject the magic that Magus uses.
