And regarding your point (1), the slides also lay out the interesting case in which the typical-case asymptotic time complexity a1 N^b is far more favorable

And regarding your point (1), the slides also lay out the interesting case in which the typical-case asymptotic time complexity a1 N^b is far more favorable than the worst-case form of a2 N^b The first form is generally deduced through extensive experiments with typical data, while the second is (often) easily proved with just paper and pencil. The first is the more important in practice, but the second is what's quoted in textbooks. There are so many algorithms in which a1 << a2, which enables all sorts of problems to be addressed that would be otherwise intractable. The linear programming/max-flow type problems the slides mention are a major case.