It seems to me that you could still tell a few things. If it’s shaped such that it would have been attached to wood or leather pieces, for instance, then you might be able to conclude that it’s old enough that the organics have rotted away. And for an obsidian tool in a volcanically-active area, the time since it solidified might give you an interesting upper bound on its age.
Interestingly, obsidian can be fingerprinted to identify which volcano it came from. Many obsidian tools are found hundreds of miles from the source of the stone. And there’s this: Obsidian hydration dating - Wikipedia
But in general a stone tool sitting on someone’s desk with no information about where it came from is worthless scientifically.