Carpentry already has a quest requiring adding a stone to a cane (Level 45 - Jade Crook) - However, for that particular item, you need an untreated Jadeite. Perhaps polishing the stone or whatever goldsmiths do makes the stone unsuited for CNJ purposes.
The way I see it, if you're using a weapon of one, you can't use it to focus on magics of the other because of the training used in CNJ/THM requiring either an organic component (primarily wood, some stones can be added to it but only by skilled carpenters) or dead/unliving components (polished stones/horns/bones).
It's kind of interesting how the contrast exists even in the craftsmanship of the weapons.
The way I see it, if you're using a weapon of one, you can't use it to focus on magics of the other because of the training used in CNJ/THM requiring either an organic component (primarily wood, some stones can be added to it but only by skilled carpenters) or dead/unliving components (polished stones/horns/bones).
It's kind of interesting how the contrast exists even in the craftsmanship of the weapons.