I don't recall any serious poke from my wire fencing.I know what you mean. I have done that myself on all kinds of fencing. Works great most of the time.
Having said that, I think I'm moving to using zip ties these days for many things. Easier to work with. I only take out the heavy wire if something really needs all that extra strength.
Have you ever been poked by bending that wire over to attach fencing together? I have. One time I even got poked through my leather glove. The was no fun. In contrast, I have never been poked by a zip tie.
Now HARDWARE CLOTH is another thing! I had puncture wounds and bruising through my clothing from that fencing.