A few years back I used some of my single spun wool to make a bonnet. The wool was quite dark in color, and does not photograph well.
I’ve since made another bonnet, this time using some commercially spun linen. The pattern is based on a bonnet in the collection of the Danish National Museum in Copenhagen. The pale color in the linen makes it easier to see the stitches.
Now, examining historic hair nets, some of them were made from tightly spun singles. I experimented with some tightly spun wool, not treating the overtwist, nor waiting for it to settle down. It worked just fine. The weaving was easier than I expected, not really hampered by the extra twist. The finished piece, well, yes, I soaked it and blocked it twice, but it looks just fine.