While you are right that historically there are no evidence of swords on back, it is neither impossible, nor fully impractical.
Here is a video that shows that modified scabbard can allow this, and why whould you want to do this.https://www.youtube.com/watch?v=0EWi2DnDoaI&ab_channel=Shadiversity
But I shure think that rapiers, axes and maces have no place on your back.
Very interesting and creative indeed! But be aware of what we are doing here, we are coming up with reasons and solutions to make it plausible and possible, while hundreds of years of martial arts never even bothered talking about it, not to mention creating very complicated scabbards to make it work. As much as that guy in the video tried hard to justify it (and he made some compelling arguments and built some solid prototypes) he didn't go to war with his contraptions.
Obviously I didn't either, but there are two major points that make a sword by your hip clearly better (and are not up for debate due to laws of physics): it's in your field of view and you can draw it quicker.
When it comes to implementation in BG3, it would be fantastic to have both, with an arcade/realistic option in the game menu.
In any case, thank you for the video! It's amazing what people come up with when challenged.