SICP is overrated to whom? For me, it was the most profound and wonderful educational experience of my life. I found it to be profoundly inspirational and educational. I found it to be beautiful, uplifting, moving, rewarding, and just incredible in all sorts of ways that I cannot even begin to express. And it pumped up my joy of learning in a way that survives to this day, decades later. There are not enough words in the English language for me to express how much this course meant to me and how much intellectual joy it provided me.

Of course, YMMV.

As to what I should and should not do, who are you to tell me that?

Mathematically, immutability is more fundamental than mutability, as the mathematical models for computer programs all model mutability in terms of immutability.

Pedagogically, either approach seems to work. Which one is better? For me, the functional approach was FAR superior. The best pedagogical approach is almost always the one that is the most inspirational, and SICP truly inspired me. I found it to be beautiful, whereas I found the more traditional approach to be merely workmanlike.

Having received both kinds of education, I'm qualified to say which worked better for me. Is my experience representative? Well, lots of people who have learned via this approach seem to agree with me. Zillions of people LOVE SICP. On the other hand, zillions of people swear by imperative approach. The best approach then might vary from individual to individual. There may be no one-size-fits-all education. But I suppose that we cannot rule out that future education researchers might show that on average one approach is better than the other. The Logo people claim to have done such research for children, and they settled on the functional approach. But children are not adults, and I'm sure their research did not reach the level of proven fact.

As to which approach results in engineers who produce the highest quality software, I believe that having a deep understanding of the functional approach results in higher quality software, and the best way to acquire such a deep understanding is to start with it from the very beginning. I am not prepared to prove this assertion, but neither are you prepared to prove its contradiction.

As to which approach is closest to the hardware du jour, who cares? That has nothing to do with anything, unless you are writing in assembly language. I will point out, however, that today's hardware comes with multiple cores, and this tend is only likely to increase. Functional approaches to programming result in very natural extension to multiple cores, while with imperative styles, not so much.