Frankly, we have no real reason to believe the obsidian has special properties. It could just be a 'good luck charm.' Since obsidian = volcanic glass, and ashmounts = active volcanoes, the assumption that there isn't much obsidian lying around is not necessarily a good one to make.
And do we actually know that Reen had anything else that he took with him? I don't recall. And even if he did, it's entirely possible that he was leaving in a rush (being chased by Inquisitors and all) and just grabbed for his possessions and missed the obsidian. I don't see any reason to believe it's significant.
Here are our options.
Insignificant obsidian - enough said.
Significant obsidian - What the heck does it do? Is it like a super duper Ruin-reducing device? Anti-inquisitor charm? All in all, it isn't necessary for the obsidian to be significant. If I am wrong, you can laugh at me and say I told you so. However, until then, this is my stance.
Besides, Reen was 5 once. And if I have a pencil and I see a cooler pencil obviously lost and abandoned, what am I going to do? So, if Reen has cool piece of obsidian and sees a cooler one...