That might be true for some people from wealthier regions but I'd be surprised if that were the case for people from poorer backgrounds - even in wealthier countries. Plus it's not as if we don't have a whole plethora of multi-purpose tools from Swiss army knives, to drills that can also be used as electronic screw drivers, and even hammers that have nail pulls on them.

I suspect the reason most archaeological finds are attributed to a single purpose is a much simpler one: it can sometimes be hard to derive an accurate description for a lot of tools when you're only looking for a single use. Trying to find multiple uses is therefore going to be an order of magnitude harder. So you therefore go with the most easily identifiable use case.