I imagine that she gets these documentaries because being accused of murdering multiple babies is likely perceived by society as the worst of crimes. Added in that she was tasked with caring for these babies produces an added layer of horror and revulsion. And sadly this sells newspapers.
Though I agree with you that any miscarriage of justice deserves attention.
As for your other points, the suggestion that she was mentally unstable (is this related to the notes?) seems to apply to the periods after she was accused. Considering my above point, I imagine anyone would become rather 'unstable' if they'd repeatedly been accused of such a crime.
I haven't read anywhere that her practice was 'exceptionally poor' and in fact she was known as very diligent. Even colleagues, when hearing of her arrest, apparently exclaimed ' not lovely Lucy'.
As for the poor defence, that is inexplicable to me though I believe her solicitor was from a small practice local to her parents and her barrister could only work with the information he was supplied. There is also the possibility that the medical 'evidence' was not understood.
I am happy to be corrected on any of the above points as there are posters much more knowledgeable than me on here!