It's easy to understand why it happened when you look at the events from start to finish, going back to before Letby qualified to look after babies needing a higher level care.
2014 - Baby Noah Robinson died after a consultant (one of the 7 involved in gathering evidence against Letby) misplaced a breathing tube, placing it in the oesophagus. Noah's parents noted at the time that the unit was grossly understaffed, leading to tests and X-rays not being reviewed for up to 7 hours. Only one senior doctor was on duty on the ward, and their time was split between NICU and the children's ward. Warning signs of Noah's deteriorating condition were ignored. (Note - Letby did not qualify to work with high-needs babies until 2015 and was not mentioned in the inquest of Noah's death). Someone more suspicious than I might wonder if this is where Jayaram got the idea of air embolism from, as it was Jayaram who first brought this up, not a pathologist or the police.
June 2015 - The death of baby A is noted as the start of a spike in deaths in the NICU.
July 2015 - Breary begins his own review into the deaths of baby A, C and D, and C. He noted Letby was on shift and raised this to a manager. There is no evidence to show he considered consultant negligence in light of baby Noah, or the declining state of the hospital itself. Letby was the most senior nurse, so naturally cared for the sickest babies. She also worked the most hours.
December 2015 - COCH is ordered to pay Noah's parents £8m in damages.
Feb 2016 - A review by the Royal College of Paediatrics and Child Health shows the unit had insufficient senior cover, junior staff (read the consultants) had a reluctance to seek advice when needed, and the unit had poor infection control. They found nothing to suggest deliberate harm.
June 2016 - emails between Dr. Stephen Brearey, Dr. Ravi Jayaram, Dr. John Gibbs, and Dr. Murthy Saladi show they began discussing Letby as a potential suspect in the deaths, again ignoring the state of the ward or the consultants themselves.
Jayaram brings up air embolism as a possible method of murder.
Late 2016 - Lucy files an official grievance against Breary et al after she is removed from the ward due to repeated accusations from them.
The CQC downgraded the unit after a report found the unit to be understaffed and under-resourced.
Jan 2017 - The hospital review board ruled in Letby's favour. Breary et al are forced to apologise to Letby.
May 2017 - after having to apologise, Breary et al push managers to contact the police.
The police then rely on testimony from Breary et al to form their case, including Jayaram's suspicion of air embolism. They do initially ask various experts for their help, but ultimately decide not to go ahead with them after none of them find evidence of murder.
Dewi then volunteers on the basis that he can "solve the case over a cup of coffee" and that he "knew she was guilty from the start", i.e he is working backwards from murder and looking for evidence to fit his theory. He changes the causes of death frequently during his initial investigations to fit Lucy's shift pattern and comes up with the theory of air embolism after reading police notes on Jayaram's theories.
It wasn't that they all sat around and decided to blame Letby for the hell of it; it was a whole clusterfuck of self-preservation after witnessing a colleague investigated for negligence, an attempt to prevent HR involvement in their own conduct, and a series of poor decision-making by the police.