Ofen, when making such an argument, the advocate is describing genuinely important findings by eminent researchers. The problem arises with the way the studies are combined and interpreted.
For exmaple, each of the four above descriptions of studies (and I'm sorry, I didn't have a chance to add in specific references for this example) uses entirely different, uncorrelated measures, to measure entirely different traits. The Gee-Whiz EI argument, however, is based on one of the popularized, broad EI definitions, and lumps all the different findings together as if they made the same point.
In reality, the logic of the Gee-Whiz argument revealed, is something like this:
The logic, in the abstract, of the Gee-Whiz argument...
Study 1 uses measure A of Trait B to predict an important life outcome, outcome C -- and that's important.
Study 2 uses measure D of Trait E to predict an important life outcome, outcome F -- and that's important.
Study 3 uses measure G of Trait H to predict an important life outcome, outcome I -- and that's important.
Study 4 uses measure J of Trait K to predict an important life outcome, outcome L -- and that's important.
Measures A, D, G, and J, and Traits B, E, H, and K can all be combined -- wow that must be important!
The Gee-Whiz EI argument fails to recognize that one can't make an argument about a coherent thing -- emotional intelligence -- by combining together studies that use different, often uncorrelated, measures to measure different different traits that predict differnet outcomes.
One could use the above evidence to make the claim that a number of important relationships exist in psychology among various measures and important outcomes. One could further make the claim that there are a number of important psycho-socio-emotional relationships in life. One cannot, however, claim that EI is important, just because some popular-press definition of the concept is so broad as to include just about every social, emotional, and psychological variable studied by personality and social psychologists!
Consider the following analogy as a way of making this still clearer. Let's say that one wished to claim that Vitamin X was a powerful new vitamin. An appropriate method of proving this would be to study valid measures of Vitamin X that defined Vitamin X in the same, specific manner, and then to use those measures to see what high and low levels of Vitamin X predicted.
To continue with the analogy, the EI proponent above, however, would in this case claim that Vitamin X can be defined as including Vitamin A, B, D, and K (but, arbitrarily, not C). Each of those vitamins predict important health benefits, therefore Vitamin X is the most powerful of them all! The problem is that Vitamin X is left as ill-defined. In fact, it isn't anything at all. It would, of course, be okay to say that vitamins as a whole are important, just as, above, it is reasonable to say that personality or psychological variables as a whole are important.
One cannot conclude, however, that Vitamin X is important, because it is just a sloppy way of referring to several quite different vitamins.
Similarly, one cannot conclude that EI is important from the Gee-Whiz argument, unless one is willing to label all of psychology the study of EI. I don't think most psychologists would find that useful. Psychological terms may not be perfect, but they have been developed by very smart, analytic people over the course of more than a century, and they are much better, on the whole, than the popular definitions of EI.
Of course, there are ways to make a more sophisticated argument for EI. Such an argument would define EI clearly in a single fashion (as I do on this web site, for example -- as an ability involving four areas of skills). Such an argument would then go on to identify a measure or class of correlated measures (such as the MEIS, and MSCEIT) that employ the same measurement approach (ability-testing of a group of related, clearly defined, areas of emotional skills), and then see what those measures predict. That is what the research program with the MEIS, MSCEIT, and related measures is all about. Using that approach, EI turns out to exist, and to be important, but the picture that develops is quite different than what one gets from the Gee-Whiz approach described above. (The best summary to-date of EI as defined and measured as an ability, can be found in the 2004 Psychological Inquiry article "Emotional Intelligence: Theory, Research, and Findings," available in the "Reprints" area of this web site -- careful, it is the first of two articles in the journal.)