I always keep my weaving wire on the spool unless I have to cut it because I have to go through any holes. I don't know if it makes a difference how the wire is put on the spool, but I found it works better for me on the higher spools from my favorite wire supplier than the flat ones if you know what I mean. It probably has to do with the weight of the spool plus wire as well.
I can't work with wire that is on the spool; I measure how much I'm going to need, add a couple of feet and cut it. If I'm careful, I don't have too much trouble with tangling or kinking, but if I forget to keep my eye on it, that's when I get into trouble.
I've found that running the kinked wire thru the jaws of my taped pliers a couple of times straightens it right out.
Of course another reason to keep the wire on the spool would have been Ponder. A loose wire end hanging down on the floor drove him crazy - and not always in a good way. Gundel started doing that with my long threads now. Those cats really have a baby and a predator side!