I can imagine a pieced minky quilt would be a challenge with lint to clean up. However, I made a quilt for my husband with minky backing and he LOVES it. While making it, I used a pet hair roller to pick up the fuzzy lint after cutting the piece, rolling it over the minky edges to pick up any loose pieces that stuck to the minky too. It picked up fine. Then, I delivered the quilt to my LAQ who said she had no problem quilting with it. I kept the edges longer so I could turn them around to the front and fold/sew the binding and complete the quilt. Turned out great. He uses the quilt alot over the past 2 years and we've had no problem with it.
Meanwhile, since then, I made a quilt for myself with good quality flannel backing. It's nice. But, I prefer the feel of the minky as it's so soft. I'm sure a minky-backed quilt will be a to-do item in the future again.