All metals will work-harden and anneal. HOW hard or how soft varies. The craft wire, as far as I know, is always dead soft, but not usually specified as such.
Not all the "craft wires" are the same. Some are enameled, some are anodized. Some have clear-coat over the color -- I've had pretty good luck with "Zebra wire" brand for a coated copper. OTOH I got something dark blue off a shelf at JoAnn's and it is AWFUL, it scratches if you look at it wrong. If you don't hate the color of copper, plain old copper wire is a good "cheap" wire to work with. It's kind of popular right now, too. Brass is also inexpensive, but the dead-soft brass I have seems harder than half-hard sterling. It's considerably more difficult work with at 16ga.
Sterling actually isn't THAT expensive and you can collect your scrap bits and recycle them. I send mine back to Rio and get a store credit for 75% of the silver market value. It can be mixed sterling and fine silver including sintered MC. So the mistakes aren't quite as expensive as all that...