It is called a "supplex" not a souffle. If we are talking about the same thing, which from your description, sounds like we are. Souffle is french word for an egg dish typically.
Anyway, supplexes are allowed in wrestling. Why? because they don't really hurt anyone, or the chance for injury is minimal. One of my students was supplexed by a All Air Force Wrestler in a submission tournament the other day in which there was "no rules" other than striking or kicking. No one was ever worried about him breaking his neck.
Oh we did disallow twisting ankle/knee locks and neck cranks in the beginners categories.
I point this out, because most grappling matches also try to eliminate that which is truly dangerous to participants for submissions.
"the squeeze around the middle" was not eliminated.
Can it happen? No question about it. Often....no. More the result of a bad position or accident rather than intent.
This weekend I submitted a guy with an eziekel choke. I saw Rear Naked chokes, I was submitted by an Omaplata, and an Arm bar...out of about 40 fights, I never saw anyone submit from a squeeze from a bear hug, or risk having their neck broken....oh yea...we also allowed slamming. You should see my face where I was slammed with elbows. Never once was I worried about my neck.
Tearing flesh is a waste of time. It pisses guys off and keeps you occupied doing something that is not immoblizing or dominating. Pressure points and eye gouges and vital areas are all good set ups to distract your opponent in a real fight...but they are not means to an end, simply a distractor to divert attention to your true attack. They can buy time possibly.
Skilled guys though will avoid them many times. I do, I am trying to control the emotional state of my opponent and mostly want him to calm down, relax, and not thrash about. Poking someone in the eye can increase his emotional state and give him an adrenalin dump which may not work in your favor.
The Gun analogy, not the same. Why? we have documented proof from the examples of others that guns, knifes, etc work if applied on a fully non-compliant person on a fairly predictable and consistent basis. I have proof that certain grappling techniques work on a fully non-compliant person as I have done them.
I can only tell you that I have never seen what you describe be effective on a predictable and consistent level.
I or "we" are not saying it is not possible. Simply that it is not commonly done or been proven to be repeatable to a degree that would warrant teaching to the common person. Paradiqms are broken everyday! It is quite possible that you are correct and that I am missing out of something.
The only thing I could tell you is to go to a submission fighting/grappling tournament and start submitting people with this move...they will tap once the pressure becomes too much. After a few wins, people will start to notice.
If any technique appears too dangerous...they will disallow it.