No, not a comment about the contents of what's inside the paper, but the actual paper itself. I demonstrated the wrapping method of propagation for a local rose society this week. The members were encouraged to bring in their cuttings and newspaper so we could process them together. I was a bit surprised when I began wringing out the wet newspaper and found their local paper fell apart like dryer lint! No matter how many sheets of paper I put together, it fell apart during the wringing part. It wasn't me, as I had brought my own papers with me, The Wall Street Journal and USA Today. Not that those are what I read, as I don't. They are what are made available to me by friends who do read them. Both papers hold up perfectly when wet and wrung out to produce the damp paper to wrap the cuttings.
So, if you're experiencing difficulties with getting your wrapping paper squeezed out, you might consider the possibility that the actual paper your newspaper uses isn't as durable as some others. You might find it worthwhile picking up a Sunday paper, or two, of ones I've mentioned, or, better yet, make a friend who reads them and won't mind passing them on to you!