Even by that logic, stone still would be better than Copper because of availability and thus used more regularly as we see in the archaeological record. If that were not the case, then we would see copper axes much more than we do and other metal industries as well (Bronze if tin as available, iron and so on) as had happened in Europe and Asia. But we do not see that.
Smelting makes copper more available due to not having to find just raw nuggets of the stuff, other minerals that are derivatives of copper can be used as we see in Europe earlier in time. With out that bit of technology, copper is relegated as a source of fascination and value to the native people of North America. Also, with smelting, casting becomes a technique used to make far more robust tools as we see in Otzi's copper axe and others from the Chalcolithic of Europe.