Everyone knows when it the SHTF most training goes out the window.
Everyone? Thats a bold statement. If this were the case, why train at all?
Appropriate training results (or should result) in "automatic response" or essentially, muscle memory/autonomic response. It stands to reason that, whatever "habits" you are constantly exposing yourself to during your practice sessions are most likely the habits you will resort to, subconsciously, when the SHTF. Appropriate training helps one to identify and apply corrective measures much faster than those who choose to go without.
This is not to say that one can predict and therefore prepare for every possible scenario out there, but it is certainly possible to become adept enough with using various techniques to the point of, essentially, becoming quite effective when under stress. Although, it is possible for one to become so overcome with stress/anxiety that all training is blown out the window, so to speak. This is mental, not physical in nature. Either way, better to strengthen the odds with training than to dismiss it as unnecessary.
The only thing I can think of that goes beyond the skill that comes from repetitive (and proper) training is the ability to adapt/create. Adaptation is, I believe, based on the individual and cannot necessarily be learned through training. Similar to the idea that you can teach someone how to draw and use the tools necessary to that end, but creativity itself is not something that can be taught to any effective degree. In this case, you either have the necessary predisposition or you do not. Regardless, training and the familiarity with the tools can prove to be very useful and it most certainly should be considered necessary if one is to demonstrate any level of proficiency, whether consciously or subconsciously.
If one is unable to acquire the necessary skill/confidence in using a handgun for personal defense (I am speaking of HD here), perhaps the use of a shotgun would be appropriate. However, this weapon also requires a decent amount of proficiency in order to be effective.
If one is not willing or able to acquire at least a basic level of proficiency/confidence level regarding their weapon of choice, he/she should very well consider not using the weapon at all (for PD or HD).