> I don’t see any use case or security benefits by using the static password feature. Even if you enter a password manually and concatenate it with the password of the Yubikey, a keylogger still gets both parts (assumption: You don’t reuse passwords).
If keylogger is what you're defending from, yes, it doesn't help. And in this scenario you've probably already lost.
On the other hand, it makes a large portion of the password immune to video-recording you typing the password in. Yes, it's technically trivial to then steal your Yubikey, extract the static password and combine it with the recorded one, but these are still quite some extra steps.
My point is, if a particular service or application doesn't support anything more refined, using a static password as a pepper[0] is perfectly fine and still an improvement over not doing so.