@Attmos in bonsai we use copper wire by wrapping it in spiral around a branch or trunk, then bending the limb into the shape we want. Using raw wire as is can be done in a limited capacity, but we often find ourselves work with lengths of wire as long as your arm or better, but by the time we're done applying it it's lost more than half that length. That's allot of work on the wire, which makes it harden. This isn't a bad thing because as it gets harder it holds the limb in place more firmly.
When working it that much, though, the raw wire as it's often found will become brittle and often break. To avoid this and give us more working time we prefer annealed copper. It goes on with less effort and allows us to adjust more as we go along. These are all important factors when you find yourself wiring EVERY SINGLE branch of a rather large tree, especially with species that have wood that resists shaping.
None of this applies to running the same kind of wire for electrical work because it's being bent and twisted minimally over what we consider extremely long lengths. The issue of work hardening just doesn't come up much in that context because you're trying to do exactly the opposite, though I'm certain you've had a licensed electrician caution you about messing with it too much to avoid breakage and shorts.
If you talk to a machinist, jeweler, or other craft metalworker, though, they often work with copper on custom pieces, and they deal with the issue of work hardening allot. We're not quite to that level, but wiring trees does routinely bring us into that sort of concern.
On the hobbyist level, figuring out how to source and anneal our own copper can have a big effect on our budget, just like other hobbies have people looking for low cost alternatives to common issues. Professionals tend to make enough money that it's worth getting purpose produced stuff that doesn't come with this level of discussion.