Hyoho Niten Ichi Ryu can also go on that list.

It certainly doesn't seem to be an unusual thing; all three styles I practice (Seitei Iai, Muso Jikiden Eishin Ryu, HNIR) do it for different reasons and in different ways. Compare Soete Tsuki from Seitei Iai (originally from Hoki Ryu), Uki Gumo from MJER and Hari Tsuke from HNIR. All three touch the back of the blade, but all for different purposes.

Still, I think "don't touch the blade" is a requirement for anyone not practicing JSA. It certainly is a good guideline; unless you have a d*mn good reason for it, your hands just hold the sheath and the handle, that's it. Safer for the blade, and safer for the one who would touch it. Even being a JSA practicioner, I've no reason to touch any blade but my own, and just during practice.

That last part sounded kind of dirty.. eh, what you gonna do heh.

Also, you can add that rapier blades were often held with a finger on the flat of the blade to help with point control (part of the reason for the elaborate rapier hilts instead of simpler, solid ones found on later smallswords).

However, as others have said, for most styles, touching the blade is not a good idea except in very specific circumstances (a hard block or controlled thrust). First, it does put your hand at risk, not only from your blade, but your opponent's as well. Second, it means you have to clean the blade after every practice. Third, ... do you need a third reason?