Overkill

Submission holds have extremely limited application to civilian self defense scenarios. Submission holds can be faked out of. Submission holds can have severe asymmetrical consequences. Submission holds are complex movements prone to failure. Submission hold alternatives take less time to learn and are more valuable to civilian martial arts consumers.

In the South East Asian martial arts we sometimes see the "Principle of Overkill," were they refuse to stop attacking after the opponent goes down. These arts aren't training for casual bar brawls to defend the honor of open minded girlfriends, these arts are training for life and death combat between rival feuding parties. One sneaky strategy is to fall down early in a brawl, act incapacitated, wait until an opponent is not paying attention to you, then pull your knife and attack them from behind. Because of that these arts specifically train to overkill a downed opponent, to make sure that opponent isn't being sneaky.

The application to this for submission holds is obvious: in a serious self defense situation, what do you do when your opponent taps or says "uncle" or "ok, I give up, sorry!" How do you know they have sincerely repented and aren't going to attack again? How do you know if they just realized how outmatched they are and are about to pull a weapon?

The obvious alternative is to turn the hold into a full damage attack, dislocating a shoulder, breaking a leg, or choking them unconscious. This cure can be worse than the disease; the consequences from going that far can be worse than whatever the attacker was trying to do to you in the first place. Prison time itself can be life threatening. Any allies they have who are prone to drastic violence aren't going to soon forget that you maimed their friend. What happens if you hold a choke too long because you were worried they were "just faking it"?

That's assuming the submission hold works in the first place: all submissions are more complex movements than most strikes. Beyond that your mobility is compromised while you are executing a submission hold. Even if you somehow manage a submission hold while up on your feet, you are still giving up options to run or otherwise maneuver as long as you are applying the hold.

"But why not use a submission hold to control someone until authorities arrive and arrest the attacker?" Let's put aside the problem with the attackers friends showing up before law enforcement, and instead ask if a submission hold is actually the best way to control someone. Many grappling styles have various pins and other control positions that are far less complex and thus more likely to work than trying to use a submission hold. "Position before submission" is a best practice for grappling arts anyhow, and position is more key to controlling the attacker, not so much joint locks applied thereafter. 

Training for superior position both on the ground and on your feet is much more valuable to the average civilian martial arts consumer than learning submission holds. If a well thought out self defense paradigm is used, grappling instruction can improve a civilian's mobility in a real confrontation instead of compromising mobility: