I agree about the bobbin being a waste of space. Also a thread that is tightly wound will tangle easier, which is why some hand sewing threads are wound around giant spools, it makes the thread easier to handle. Fishing line is probably on large spools for the same reason.

Winding it around a film canister or similar container with a rubber band to hold the ends down sounds better to me, or winding around a flat "card" for a low profile, although that means time consuming winding by hand.

The nail idea is great, a nail has many uses and adds value to the storage.