Well, yes, but leaving the limiting of rare materials to the DM isn't suitable for every table IMO. My players in my last 5E campaign were really into crafting, and when I tried to limit their access to crafting, it'd make the game unenjoyable for me and for them, and they tried to circumvent the limits in every possible way. For instance, when the players wanted to craft a Headband of Intellect, I said they'd need to go on a side trek to an island full of psionic monks. So the main quest was put on hold since the party wanted this item really badly. Not only that, but when the players found the psychic crystals out of which they could craft items, they didn't try to get one. They wanted to harvest enough materials to make multiple items, and I (unwisely) said they could roll to see how many they could get. The result was that the party got not just one, but two Headbands of Intellect.