The main use for wire (copper, brass, or iron/steel) is to bind things together or to hang things over a fire. Yes, snares were/are made from them, but do take a little learning/knowledge to make and use. And copper/brass wire just doesn't rust, or corrode as fast as iron/steel. Copper wire tends to be softer than brass, and both tend to be softer than iron/steel. But all can be hardened up if necessary.
The old lists of trade goods for the Indians in North America showed a lot of copper/brass wire being shipped out to the tribes. They used it for all the uses already listed, but also used it to wrap knife handles to hold them together, and as decoration on tomahawk handles and pipe stems.
Having some wire along is kind of like having some cord/rope/fish-line along. Once you have it along, you will be finding more and more times to use it.
Mikey - that grumpy ol' German blacksmith out in the Hinterlands