If you are going to wind an electrical coil (to make an electromagnet, etc) then spring-back should not be a problem. First, the copper wire is not supplied hard-drawn but fairly soft, and second, it is helpful to varnish the windings and possibly tape them too, before removing tension from the coil.
If you are winding a resistance or heating coil, there is still no need to use hard-drawn wire, but of course you will not be producing a tight coil as air must circulate.
Cheers, Tim