I don't think explicit instruction can actually "reprogram" a social ignoramus into a masterful manipulator, but arguing that it's not a good idea to teach people the basic tools to understand and manage their own (and, to some extent, other people's) emotions because it might turn them into something they are not is akin to arguing that teaching things like critical thinking skills, or reading, is counterproductive, because people might access and consider new ideas and become something they are not as a result.
I don't think that not understanding what's going on or not having tools to handle a situation is ever a better option than understanding and having the tools.
And as far as having high EI be counterproductive to your occupation... Yes, it's absolutely true that focusing too much on the "human side" of an occupation that doesn't have much of one will actually make you less effective at your job. However, an accountant or a scientist or a mechanic still goes home at the end of the day and becomes a parent, sibling, friend, child, spouse, etc, and I'll just bet emotional intelligence actually helps in those occupations. Yeah, it's unfortunate that sometimes self-selection bias doesn't steer people into the optimal occupations for their skillset, but, once again, improving the overall emotional intelligence of large populations through some basic instruction will hardly make people less able scientists, accountants, and mechanics, and is more likely to simply equip those whose skills are deficient to better deal with things like office politics, which even accountants (and definitely scientists!) have to deal with (and probably help mechanics with customer interaction).