While kansetsu waza (joint locking techniques) and shime waza (strangulation techniques) have been an integral part of classical Jujutsu, the idea that Osae waza (pinning/holding techniques), at least in a Judo context existed is simply wrong. Kano has said in much of his writings that most of the newaza of Kodokan Judo came from Western wrestling and/or invented by him. Remember, the battlefield of ancient Japan was a massive melee fight in which many folks were running around with swords and other sharp pointy things trying to kill each other. They were not going for submissions or for the other person to run away with a bloody nose, they were trying to kill each other. Instead osae waza of classical Jujutsu was designed to hold the person in place long enough to use your own weapon and dispatch your opponent while remaining in a less vulnerable upright posture alert and ready to deal with other warriors on the battlefield (zanshin).
So the notion that someone on the battlefield wearing full armor would lay on top of someones face using Kami shihogatame and smother them in the heat of battle is one of the most absurb things I have read in months. I mean think about it. The helmet that is likely being worn has a brim at the front that extends out in front of the face by several inches. At the back, you have the sloped rear of helmet that partially or completely covers the neck. It also extends out from the head by several inches. Now press someones head who is wearing this type of helmet to the ground, and you cause the helmet to shift on the head by several inches making the separation between the edge of the visor and the face many more inches. Now let's get to the guy doing the "smothering" technique. He is wearing armor on the torso that would include a hard breastplate, and semi-flexible plated armor (which run vertically in plates) below that. Now, how do you suppose that the guy on top is suppose to get a clean seal over the mouth and nose of someone on the bottom when the brim of the visor sticks out probably six inches or so, and he is trying to lay an inflexible sheet of armor on top of his face? Probably not real likely that this armor is going to deform sufficiently enough over the extended front of the helmet to allow them to cover the mouth and nose. So let's assume that he manages to get an adequate seal over his opponents mouth and nose. How long do you think he will need to lay there and wait for the other guy to sufficate? Many folks can easily hold their breath for 4 or more minutes. In the heat of battle with the heart pumping hard, maybe two minutes. That is a LONG time to be laying prone on the ground when there are others on the battlefield with swords and other sharp pointy instruments. No warrior in his right mind would lay there in a vulnerable position like that waiting for the other guy to sufficate. It is pretty likely that he would find himself run through by some Ashiguru (the lowest ranked foot soldier armed with a spear) or some other samurai would lop off his head. Contrary to the romanticised nonsense that many think of the samurai, they would not have waited until the guy got back to his feet and announced his ancestory and ryuha lineage. Instead, he would have cut apart as he laid there.
The reason that you find newaza being taught today in modern and semi modern Jujutsu systems is really quite simple. First, many of the instructors that teach these systems of Jujutsu have a background in Kodokan Judo. Second, much of what is called Jujutsu today does not derive from classical Jujutsu, but is instead modified versions of Kodokan Goshin Jutsu (which is basically Jujutsu techniques for the Judoka that were developed within the context of civilian self-defense and not battlefield fighting) and third, the popularity of Brazillian Jujutsu has lead many instructors to incorporate Kodokan Judo newaza into their curriculum to satisfy the market of students who are looking for and expecting this part of Jujutsu in their training.
Anyway, sorry for the rant. After reading some of the above comments, I just could not contain myself. :asian: