If you have Jack Dempsey brand broadcloth blocks, they will outlast any 100% cotton that you put with it. Not associated with the company, but have used a lot of their stamped goods.
I, too, have made many a quilt with Jack Dempsey quilt blocks. I am sleeping under a quilt that my aunt made about 30 years ago and it is washed regularly and is in perfect shape. Here is a quilt that I made for my DD using the JD blocks - but, it has never been used or washed:
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