I don't think it's impossible to have both high levels of "traditional intelligence" as you have termed it, and emotional intelligence. There are two types of intelligence: fluid intelligence, which is a persons natural ability, which many psychologists have argued is predominantly hereditary, and crystallized intelligence, which is stuff we have learned from books and life experiences ie. knowledge, which constitutes the intellect.

Emotional intelligence is a different animal, but not necessarily an adversary of fluid and/or crystallized intelligence. In fact, within a well integrated, self actualised person (Maslow) you can expect to find high levels of all three types of intelligence, and displaying a cold, rational intellect that seems devoid of all human feeling does not mean that emotional intelligence is absent or lacking, it may simply be an indicator of an optimal functioning intellect which views the containment of emotion as conducive to expressing oneself articulately and clearly, and without the contamination which emotionality can sometimes cause.

I would not be willing to sacrifice some fluid or crystallized intelligence to gain emotional intelligence, as despite my posting style, I am actually quite a sensitive and emotional person, but also very adept at concealing it. For me the question should be "would you be prepared to sacrifice some emotional intelligence to gain some fluid or crystallized intelligence?", and the answer would have to be "perhaps".

I value both my intellectual intelligence and emotional intelligence in equal measure, as a disequilibrium or one without the other is disadvantageous and a barrier to the pursuit and achievement of a well rounded, complete personality, and accession to the "Higher Self", which can ultimately lead to a happy, prosperous, and satisfactory life.

Btw, IQ tests are a faulty tool with which to measure intelligence, as they claim to measure fluid intelligence ie. natural ability, but the truth is many questions on IQ tests are dependent on some measure of crystallized intelligence to be answered. For example, if I had never learned to do mathematics I wouldn't be able to solve a metamathematical puzzle. That does not mean I am incapable, stupid, or do not have the ability to do maths, it just means that I was never taught and thus never learned.

The same could apply to driving or playing snooker, ..these are all learned abilities. So your intelligence quotient is an inaccurate score indicative of approximate intelligence level, produced by a test which is reputed to be biased in favour of white, middle class Western males, and which in no way should be viewed as an accurate indicator of academic ability, and despite protestations from the creators of these tests (mostly white, middle class, Western males).

The most intelligent people I know are those who know their limitations.

That's real intelligence.