That’s because the scabbard and sword is of a later era.
A common misconception is that people used to have a lot of wooden scabbards, when this wasn’t the case. A wooden scabbard hinder mobility quite a lot when the sword is drawn as it retains its rigid/erect shape. This means it does indeed hot stuff, just like when a sword is sheathed. However, for soldiers whether infantry or cavalry, or just in general this is not good.
Initially, foot soldiers will need to take up as little space as possible and maintain mobility as a unit, having these erect scabbard hinders this and puts the soldiers at a disadvantage.
Cavalry would also be hindered by this as during this era the horsemen did not affix their scabbards to the horses saddle as seen in later centuries, they wore it on their hip like any other soldier would. This means when the sword is drawn, the scabbard would become lighter whilst still erect, when at canter this then means that the scabbard starts to fly about the place, pulling and putting strain on the sword belt itself as well as looking stupid and hitting the horse (this can have many effects, spurring them on for example, or spooking, of distraction. All of these lead to a lack of control over the animal, which is not good.)
Finally, having a wooden scabbard lined in leather and wool is just simply more expensive than a simple leather scabbard, or perhaps of you’re being fancy, a leather and sheepskin scabbard. Why bother spending more money on something that is ultimately a hindrance and not very useful?
For example, all of my swords / weaponry requiring scabbards are just simple leather scabbards as they simply work well in doing the job of a scabbard and also look nice (as well as authentic.)
Unfortunately, with the lacking of resistance when the sword leaves or enters the scabbard, there is no cool noise such as schwing or thunk/clunk. The most it gives is just a noise of basic friction against a non-smooth soft surface.
I am not denying the existence of wooden scabbards that is, there are indeed examples and evidence that does support their use, but never in vast quantities. The problem with a leather/and sheepskin scabbard is that they degrade quicker and we are sometimes left with less evidence than there should be; however we can reference most tapestries to see that a lot of the scabbards (that I have seen (northern/central Europe)) do not have wood in them (we think.)
If in doubt, go check your national archives and see what you can find!
Edit: written late at night. I see some spelling/autocorrect mistakes. Too lazy to fix them.