Instructing and training someone who may find themselves in a desperate fight protecting their life, or that of an innocent third person, requires them to learn to operate their handgun so that they can exert superior control, operation and retention of their weapon during both 1 & 2-handed shooting. The conditions and circumstances in which they may have to accomplish this may vary according to events.
Not everyone has the same size hands, the same degree of physical dexterity, hand/wrist strength, etc.
Some handguns are going to place different demands on different shooters. (Size, weight, caliber, design/action, etc.)
Just like martial arts practitioners may not be able to make one response and technique work for all possible conditions and circumstances, a shooter may benefit from acquiring some flexibility in learning to master a "grip technique" that enhances their ability to control their weapon under various possible conditions.
There's no "rule" that excludes fluidity in the performance - and subtle shifting, if need be - of the "best" appropriate grip technique for the needs of the moment.
If someone only works to learn one specific technique, will they be able to meet a sudden critical demand to safely, efficiently and effectively run their handgun 1 & 2-handed using their dominant hand, as well as 1 & 2-handed from the perspective of using their non-dominant hand?
Seek the training you think you may need for your anticipated circumstances ... and then practice, practice and practice some more until that technique (or range of technique options) is accessible without "stopping" to think about it under stress and duress.
Then again, some folks might only need and wish to enjoy some leisurely target range sessions.
Most people who drive motor veh's will never find they need to be trained to be as skilled and capable in their driving skills as a race driver. Many drivers may discover, to their dismay, that they may lack the necessary skills to respond to an unexpected emergency driving situation, though, let alone do so effectively and be able to make the right decisions.