It's true that a catchy headline does help to make science more accessible to the general public. But this should come in addition to, not instead of, accurate descriptions of the progress made. With the current headlines that focus on being "more adjective than previously thought", there's a tendency to paint the previous thoughts as wrong. While some public humiliation of what had been previously thought can sometimes be necessary, this should not obscure the truth of the research.
An accurate headline could often be an improvement in the public's understanding of scientific research without creating an over-simplified narrative of science. Instead of "X is more Y than previously thought", headlines could use phrases such as "X shows a nuanced improvement in Y" or "X presents interesting possibilities for Y".
As Nikhil highlighted in his original essay, scientists make incredible leaps with their research; they don't just slightly improve on each other's work. For this reason, the progress made through scientific research should be communicated clearly and accurately, rather than through a sensationalizing headline. Otherwise, we miss out on the full potential that comes from truly groundbreaking discoveries, and their novelty is lost in "public humiliation" of what had been previously thought. UrRong about making small but significant advances in research more accessible to the public, headlines should also reflect the revelatory nature of real scientific progress!