A control technique (or more appropriately an "arrest/control technique") is a say-uncle type of maneuver that is common to Jujitsu (both Brazilian and Japanese), Judo, and Aikido. The attacker is generally subdued through pain compliance. These techniques are perfect for law enforcement that is dealing with non-compliant or formerly combative subjects. However these techniques are not really suitable for private citizen self-defense.

Control techniques stop your escape. Since the purpose of self-defense is not to make arrests or hold people in place the application of a control technique will prevent you from getting away from the scene.

Control techniques only work while being applied. Unless a technique is applied with enough force to break something, all of the pain (and compliance) is going to stop once the technique is no longer being applied.

Control techniques expose you to multiple attackers. While a control technique is being applied, it is very hard to deal with any additional threats. At a minimum one hand will be occupied maintaining the technique, reducing the possible responses to a second or third attacker.

Control techniques don't have an exit strategy. So you have compliance, now what? Unless you have a set of handcuffs as soon as you let go you are back to where you were before got the hold in the first place.

Control techniques are complicated. In addition to needing to acquire a grip, you generally will need to move your whole body in order to maximize and secure the technique. This might take a fair amount of timing and coordination in order to perfect.

Control techniques that fail may place you in a more vulnerable situation. If you have committed to the the technique and it doesn't work as planned you might be in a worse position to continue the fight from where you started from.

Control techniques probably less force than you are being attacked with. A violent assault probably merits a stronger response than a pain compliance hold.

Control techniques can be difficult to learn and even more difficult to master and apply successfully. That time, money, and effort can usually be used much more efficiently on other, more effective techniques. Like being able to run a mile.