“Wear” is the correct term.
Carrying a blade on your belt, (usually on opposite side from your dominant hand) is an entirely practical consideration. It’s not really possible to draw from the back in combat. You can do it, but it involves either some juggling of the blade, or unslinging the scabbard, pulling the blade, and then returning or discarding the scabbard.
Alternately, you can simply reach across your waist and draw a sword. Faster, simpler, easier to do in combat. It’s also going to be out of your way most of the time, while one on your back could become an issue. Finally, while drawing it, you’re putting the blade between yourself and your opponent almost instantly, which can have sometimes have applications in defensive situations.
It’s hypothetically possible to design some kind of scabbard that would hold a blade on the back for easy access. For instance, a sci-fi setting where they use strong electromagnets. It would also be possible to store a collapsing sword on the shoulder, or across the small of the back.
In the real world, slinging a sword (or other weapon) across your back usually meant you intended to ready it before combat, rather than during the melee. Remember, historically, swords were actually a sidearm, and almost never used as a primary weapon. So a soldier would need their sword someplace they could get to it quickly, should their primary weapon (usually a polearm or ranged weapon) fail.
If your character carried a sword as their primary weapon, for example a Zweihander or claymore, then it’s entirely possible they’d carry that across their back, with a sidesword on their waist while traveling. Before a battle, they’d unsling their primary, prepare it for use, and then put their scabbard with their kit. If they were ambushed on the road, it’s far more likely, they’d simply use their sidesword, rather than trying to get at a weapon on their back.