I don't use cheap batting and still get that, perhaps not as bad you described, but bad enough I had to do something about it before washing. When I wash them without removing the lint and fluff, it doesn't always come off, but instead pills up.
I just use a lint roller when I am through and not worry about it during the process. Since I have cats who love to lay on my quilts in progress, I would have to use the lint roller anyway.