That is frightening. I can't think of any function I write without taking a second to think about what the Big-O would be.
And I don't even know how I could do things like parse input without knowing how to structure it so that look-ups never take more than log N time. And I don't know how I could do that without knowing sorting algorithms intimately.
And I am not writing codecs or kernel code, mostly it has been high performance and some soft real time, but I've also worked in back end web development.
Everything in your second paragraph I fully endorse, but your first paragraph is terrifying. I'm terrified I'll run into someone like you some day, clearly smart, clearly experienced and without a clue as to why I'm concerned about the Big-O of his implementation of something.