when I've done paper piecing for wall quilts I didn't take the paper out at all.
Some antique quilts have been found to have newspaper or catalog paper still in them. I don't think paper was so acid then though. I wouldn't leave it in for a quilt I was going to use, but on the other hand paper just goes soft when it gets wet...
Please don't get overwhelmed by the number of pieces. Like anything else in life you do it one piece at a time