It doesn't have to be a conspiracy as such, scapegoating can occur through groupthink, and it's possible the doctors who started the ball rolling genuinely believed something was amiss. Or were indeed covering their own backs. This is the big problem with the whole case IMO. Why her? The most logical answer is that she was there, but that's the sum total of the evidence until Dr Evans swans in with his ten minute coffee imbued analysis.
And then the retrofitting commenced. We are suggestible creatures. The parents, already in a heightened emotional state, and trusting of the police, would naturally be looking back on an already traumatic experience, now being asked to revisit it, sometimes years down the line, with an extra and unprecedented layer of horror. I do feel the most sorry for them in all this. They too have been psychologically tortured by the mishandling of this case.
This all began with an uptick in unexpected deaths / incidents in a relatively short time that of course should be looked into. We know the ward was understaffed, rounds weren't done as often as would be imagined on a unit supporting premature babies, etc etc not to mention the sewage issues. Any one or all of these factors could - and initially did - explain it all. But only after Lucy Letby was removed from the unit was it downgraded and other issues addressed, so it conveniently appears as though it was her all along.
One can actually build quite a convincing case for conspiracy when you think about it. And what for? Money / reputation are the usual motives.
Additionally, the system is a juggernaut - a point is sometimes reached where it almost takes on a life of its own where no one person or even agency has the power or will to call a halt because enough damage has already been done, so it may as well be allowed to play out to its conclusion. This is where we need proper re-examination of the system as a whole and its handling of complex multi-faceted cases.
I think one can swing back and forth on the conspiracy angle, and it may well depend on one's definition of conspiracy - does it have to be downright malice towards a scapegoat, or a series of panicked and ill thought out actions by a few people doing some arse covering and with hero complexes who then had to double down to save face?
All I know for sure is that my faith in this country's institutions was shaky at best, and now is non-existent.