The common reasons I've seen for Japanese swords commonly worn and drawn edge-up (the most famous example) are:
There are likely more, but I can only recall these. I'm really skeptical about the true effect of these upsides (or if they are even present or not). If the upsides are significant then no sane soldier would ignore them, yet I have never heard of this practice being popular outside Japan.
Or is wearing and drawing edge-up more common than I think?
This is a hard one to answer completely with references to historical sources simply because the Japanese are the only ones that talked about how to where a single edged sword as far as edge orientation, as far as I know. What you can do is make inferences, and theorize on why we only see this in Japan. I’ll make comparisons to what I have more knowledge in, European swords, and try and shed more light on the topic through that. (Sorry if this is hard to follow, I am a bit under the weather lol)
The edge won’t dull - from my practical knowledge through HEMA (historical European martial arts) my own handling, and usage of swords, knowledge of their construction, and so on, this is only really a problem for Japanese Katana (and even then I’m skeptical about it) See, the way Katanas are historically heat treated (clay on the back of the blade and quenched in water) the edge is EXTREMELY hard and allows for a very sharp edge, but it is also quite brittle. If you were to parry a blow with the edge of a katana it would more than likely chip (this is why in their martial arts they tend to use the flat of the blade for parrying if I am not mistaken) but when contacting wood, or horn from a saya I don’t see this being an issue, even with repetitive drawing, the dulling would be very negligible. But they did it this way for a reason so honestly we don’t know, it could also be them just taking extra care with their edges as they tended to do 🤷🏻♂️
You can draw faster - This is honestly just personal opinion, and preference, and is what the Japanese went with in their martial arts involving the Katana. I’ve done this myself with Katanas and European swords and I have found no difference in the draw speed. Draw speed is almost exclusively tied to training/repetition.
You can strike the target in a single motion - you can do this edge up or edge down. In I.33 Tallhoffer (a historical European sword manual) the first guard shown for sword and buckler can be interpreted as you making a guard with your sword still in the scabbard (it has other uses with the sword already drawn though too) the left arm is extended with a buckler and the right arm is across the body with your hand grasping the sword under your left arm. From hear you can drawn the sword while simultaneously attacking with either edge of your arming sword, or also drawing into a thrust (I have practiced this extensively myself to make more sense of this guard, trying to better understand it through “experimental archeology” lol) this shows that again the reason the Japanese carried their swords edge up is probably more personal preference as either orientation of the blade is practical.
You can draw while kneeling - honestly I have nothing for you on this one lol, I haven’t ever done anything with this. I suppose it makes sense, but I’ve never done it myself so I don’t know.
From all of this, I think we can reasonably infer that the reason the Japanese carried Katanas blade up, is simply do too personal preference, and due too their martial arts/fighting systems. If you want to make this all even more complicated/convoluted the Tachi that proceeded the Katana was worn edge down lol. It’s basically the old saying of “there’s more than one way to skin a cat”