I thought it was interesting when the nurse testified that after the death of a child, the staff usually give the parents privacy to grieve. Yet Letby went into the room as the mother bathed her dead child, in what should have been a private moment. The mother later said she felt uncomfortable.I think "I bathed your baby" was an attempt at kinship made by a person not understanding how the mother would perceive it.
If she is found guilty (as of today, I am unsure) I think there will be several motives, not one. I don't know what LL felt towards the parents (complex and ambiguous, probably, but not necessarily hate; a huge voyeuristic element here), and there might have been the element of Munchausen by proxy, yes, but she might have enjoyed creating brutal havoc in the hospital because she was angry with it.
ETA: I looked up some peculiar behaviors and ran into obsession with reality TV. Would not be surprised if LL checking the Facebooks of unconsolable, grief-stricken parents had some element of it.
I'm not sure about motive, but I think you might be right about there being more than one. Brutal havoc, maybe, but I'm not sure it was directed at the hospital.