I picked up some 26-gauge jewellery wire and attempted a small stitching project. It didn't really go to well, mostly due to the rigidity of the wire. The wire wasn't difficult to bend, but once bent, unbending it was not an option. If the wire becomes kinked or develops an unfortunate bend, it isn't coming out and can look pretty horrible.
To be honest, I have only made one attempt and probably did not exercise additional care in handling the write while sewing. With extra care it may be possible to effectively stitch with wire and perhaps the results will justify the extra effort. I have a couple of small projects coming up and I'll give it another try.
If I can complete the stitching using the wire, I'll post the results.