Did you notice that there's only one guy with a "sword" --and it's a dao-- but it looks too big to have use a scabbard or sheath. The main reason --to me-- would be that it would just get in the way.
Probably true. There's a reason for "carrying" position you see forms start with. In battle if the sword was the main weapon, it was were carried without scabbard. The length of the swords, jian especially, was decided by this position. It should go higher than the ear when you carry it behind the back so you don't cut yourself when carrying it. Scabbards are for transport, carry with you when you don't need to use it. Or if you need a second weapon on the battle field (but then preferably a somewhat light weapon). When it's up and in use, the scabbard is of limited use.