I have a puzzle spread out on my desk. It's a "fully interlocking" jigsaw puzzle, the "jigsaw" part obviously lacking since jigsaw and fully interlocking would seem to me to be mutually exclusive categories.
The initial intent was to find out if any pieces were missing so that I could either throw it away or send it to the thrift store. That will happen eventually. I finished three more of those before, and found pieces missing in each. Maybe better luck with this one.
At the same time I have fifteen "finished" novels on my desktop. Eight are novella length and seven novel length. Each one, in its own way, is a jigsaw puzzle.
I could happily spend the rest of my life putting together the pieces. The plot and characterization, the sub-plots and flow and all the other hundreds of pieces that must be in exactly the right place in order for the puzzle to work correctly.
Sometimes in putting together a puzzle you find a piece that seems to fit--the colors are right, the shape is right, the pattern is right, but then somewhere down the line you discover that there's another piece missing--and an extra that's just a little bit wrong.
Writing is very similar. In the initial writing I may fit something in there, then discover later that it fits somewhere else instead. Most often the initial "hole" can be filled relatively easily, but leaving that puzzle piece where it was originally placed can mean the difference between the story working and not.
Leaving that piece in the wrong place means carving or painting another piece to fit the hole made by the lack, and discarding those pieces that don't seem to fit the new structure.
Much more work, in the long run. Might as well start a new story as fix the old one.