Intelligence is hardly a knife. One can put a knife aside and try training without it to better improve the "other" skills, same is not true for intelligence. And also, isn't true intelligent people are more inclined to self-improving?
I think that declining your experiences is NOT intelligence.
I disagree that you cannot put intelligence (which in this context means mathematics and language skills, hence 'IQ') aside and practice other skills. Developing a sense of empathy and charm can have almost nothing to do with how intelligent you are. Selling a product has almost nothing to do with this version of 'intelligence'. And building a decent level of physical fitness, learning a musical instrument, learning a trade or craft such as carpentry or painting a picture have almost nothing to do with intelligence as defined here.
Lots of mathematicians, scientists and academics are hard-working, 'intelligent' people who are completely underdeveloped otherwise - there's an argument for saying that I am one... - so I think that this analogy holds better than you give it credit.
I can't help but think that you are using the word 'intelligence' in a different manner to that intended by the post. The trait that you are talking about, applying your intelligence to as many situations as you can, is closer to wisdom, I feel.
Mybe your right. To me intelligence is how one processes information, definitely not how she cracks on problems (this is "smartness"). True intelligence in my view is when one pays attention to what the world tells her and reacts accordingly. It can finally lead to wisdom, probably the absolute intelligence.