I leave the paper on until the whole top is together. It helps to stabilize the whole block, not just the outside edges.
I had one quilt top bubble up in the center of the blocks. I suspect is was due to how much I had to handle it during putting it all together and folding it up to store it during the inbetween times.
Many PP patterns have a lot of bias all throughout the block and the block centers can stretch :D:D:D