(comments by Dr. Ron Chapél from a discussion on Facebook)
Mr. Parker came to a reasonable conclusion that most seem to ignore in favor of what he called, "Horizontal Grappling." This was really big in the fifties and Mr. Parker predicted the wrestling/kickboxing popularity would return. But he also said for street self-defense purposes over the competition variety, there is a reasonable priority one must accept.
Mr. Parker had a Judo/Jiujitsu background so he was speaking from experience. He said, all horizontal grappling if it occurs on the street, would begin as vertical grappling first. He reminded me of Judo Randori where you must defend against both, and points are given for the takedowns as well as the submissions. It doesn't make sense to ignore what happens standing up, so you can train on the ground. This is what I call an "Assumption of Failure."
If your overriding philosophy is, "All fights go to the ground" then it makes some sense, kinda. But my decades of experience on the streets in rough neighborhoods as a cop tells me otherwise. In fact, it truly is the opposite.
Because of the vulnerability of being on the ground "in the hood," two guys throwing blows at each other who both go down, will disengage so they can stand up and start all over again. Neither one wants to be on the ground, and even this scenario is extremely rare.
The answer he said was always "footwork" and it is one of the least-known aspects of the arts because teachers do not have the knowledge or the labor-intensive will to teach it, and it has zero commercial appeal. I'm reminded of the uneven Shaolin Temple Floors in China littered with divots from nothing but foot and stance training over the years.
So, to concede the failure of your ability to remain upright, and concentrate your training on the horizontal ground would seem to ignore a huge chunk of street truth. If an attacker's strength is in ground grappling, of course, he wants to take you to the ground, and it's a great selling point in the business of martial arts.
So you see, Mr. Parker suggested students front load their training priorities as he placed them in the Web of Knowledge. At least it is something to think about. Ask any of my students and the one phrase they all hear in their sleep is, "Fix your feet!" for a reason.