How do I interpret "Violence is the last refuge of the incompetent"?

My understanding of this line is:

Incompetent individuals, by definition, do not possess skills and wisdom. Therefore when they have (quickly) exhausted their small arsenal of half-cocked and ill-fated techniques to solve the extant problem, they invariably fall upon violence as their last hope.

The implied corollary is that anyone using violence to solve a problem must therefore be incompetent. Indeed that is the point of this statement- it is an insult.

The whole point is that the incompetent person resorts to violence because he is too incompetent to think of any other option.

Similarly, Dr Johnson was saying that "scoundrels" invoke patriotism because they have few other resources (that they can think of) at their disposal. (Note that this is a backwards way of saying that those who readily invoke patriotism are scoundrels.)

The idiom (in this sense) is not trying to say that the "last resort" is literally the last (or first, per Mr Bierce) thing that this incompetent/scroundelish person will utilize, but that this person relies very heavily on what is otherwise a relatively unsavory option.

(And when a "normal" person refers to something and says "that's our last resort", he's not literally saying that that's the last thing that will be done, but that that's a very distasteful option, and one to be avoided if reasonably possible.)