It'd be nice to be able to like put our scraps/snippets physically in the workspace, instead of them hanging around in our inventory. Since I can't lock all of them and it's tedious to put them in/take them out of my vault.

I agree, they take up a lot of space in my inventory.

Yes, I absolutely agree. It's annoying having to keep so many items in my inventory!

At the very least, once you finish the puzzle, wouldn't it make sense for the scraps of paper to change into a new item (like "taped together message" or something?).

This. :D

I was actually expecting there to be a "finished" item once the pieces were all put together...

I am assuming the reason why they did this was so that people didn't have to turn them in and not be able to use them once the event was done, as it was with the Masquerade event. When you turned in evidence then, you had no idea if you were going to get them back or not. With it this way, you know for sure you are going to keep them.