So if we all know the sword is the soul of samurai, then we all should know how to treat our swords.
Then take a look at the following sentence.
In Japn, TRADITIONALLY we must not walk over people. Why?
In a battle field, soldiers had to proceed by walking over dead bodies.
So they (ancient people) did not want to be walked over because they were still alive and they didn't want to be considered to be the dead.
And it became etiquette, not to walk over people.
We can apply the battle field example here too. The only swords they walked over were the dead people's swords. I think that is why we must not walk over any swords.
There many be some other explanations too. But here this seems like a good explanation.
By the way, if you know that there will be non-kendo people walking around, make sure that you place your swords where these people will not walk over your swords. It is your responsibility, not theirs.
I am sure that a lot of samurai in the samurai movies lean on their sword. But... We, kendo people do not.
I was once asked as a kid how I could defend myself if I leaned on my shinai.
I should be always ready:
Carry my shinai in my left hand. Be ready.
That is what I was told.
Besides, if we lean on our shinai with the kensaki (the tip of the sword) down on the floor, it may get dirty with dust or something. Then you know what?
We hit our training partner with a dirty shinai!
There is a possibility that the thing on the kensaki gets in your training partner's eyes. Is it what you want to happen to your training partner? Or to yourself?
One more thing. A sword is the spirit of samurai, so it should be very important to us too.
Would you lean on something really valuable to you? Probably not. Let's treat our swords with tons of respect.
For those reasons, we do not want to lean on our swords.
This is also seen in samurai movies. But we do not do that in kendo. Why?
The reasons are the same as above. We should be ready for an attack, and it is pretty important to us.
We should have it where it should be...in our left hand.