The faulty assumption in the more naive approach was treating operations on infinite series in the same way you would treat operations on finite sums. The order of elements being added is important, as it does change the series, and the naive approach based on putting 0 in between each numbers like 0 + 1 + 0 + 2 + … which was incorrect. There are ways to prove it does sum up to -1/12 from what I remember though, it’s just the addition of 0’s that’s bad.
IQ tests intentionally omit any questions related to empathy, emotional intelligence and creativity, so it can favour people from the top of the pile and act as accurate perdictor of success in ruthless capitalist society. It implicitly promotes lack of those traits in individuals and explicitly promotes the definition of intelligence that’s unrelated to them. While you don’t get lower scores if you’re highly creative or empathetic person, so it’s not directly a detrimental for society and can be a useful metric for some cases like specific jobs, it’s image as sole measure of intelect is manufactured to promote “specific kind of people”, to which group many republican businessmen would belong.
I’m not disagreeing with what you said, just thought I’d expand on that.