It's similar to the concept of shaking hands with your right hand. The majority of people are right handed, so when shaking hands you present this hand and clasp to show you do not have weapons. With a sword, a right-handed person draws faster for combat with the sword on the left side of the body.
In this example, the draw motion continues directly into a first attack, followed by a second overhead attack.
All of this assumes people are right handed. If someone is left handed, they are still dangerous while shaking with the right hand or with their sword sheathed on the right. Look at the biblical story of Ehud.
It is not necessary to use a katana with two hands. Miyamoto Musashi, one of the most famous swordsmen of the samurai era, preferred to use two swords, a katana in one hand and a wakizashi in the other.
Also, ninjutsu has nothing to do with this question. A ninja does not care about ettiquette; they would be perfectly happy to kill you in your sleep or by spearing you from below while you use the toilet. See the story about how Uesugi Kenshin may have died.