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=ShadiversityBut I shure think that rapiers, axes and maces have no place on your back.