> avoiding software estimation altogether because they share the two skepticisms above

Well, to put your mind at ease, I don't avoid software estimation because I share your skepticisms (although I do), I avoid it because I've observed that it's a complete waste of time. Nobody, at least never in my 30-year career, has ever asked for an honest estimate of how long it would take to produce a software product. What they have asked for is somebody to agree that the time that they have budgeted will be enough for the (vague, still being defined and still to be defined even beyond the timeline) software project and take the "blame" when it inevitably doesn't.