I think the case, the investigation and the current situation are mired in contradiction...
We want police investigations, particularly those affecting groups that have been marginalised by them, to be open and accountable. But we also need the privacy of those affected parties to be preserved.
We want police to communicate effectively, to know how to deal with the media. But we also don't want the police to have slick media operations able to deflect from their own accountability.
It's easy to say 'they bungled the initial investigation', but truth is we don't really know what the initial investigation was. I think it was
kebabking who pointed out quite early on that, if there's a high probability that someone has fallen into a river (or vanished via river in some other way), the initial search for that person has to make compromises between preserving evidence and moving as quickly as possible to find them. It's also a river path. We watch police procedurals, dramas etc and expect that forensics can deduce exactly what happened from a misplaced fibre or a strand of hair. But the truth is that a fairly well trafficked bit of public ground, with dogs, fisherfolk, walkers etc is inherently going to be heavily contaminated.
Announcing her problems is, yeah, shit. But it wasn't 'unnecessary'. It
did fulfil the media's need for explanations as to why things weren't done in a way that fit with their preconceptions of how an investigation should work. It was what the press had been asking for, and I think quieted speculation at least from that sector. But it was also definitely a pretty fucking awful exposure of a victim's private life, with a side order of misogyny.
What I think this exposes is less police incompetence, and more the difficulty of operating in an information environment where people are used to having every answer (even if they're often shit ones) at their fingertips. Where a lack of answers is never accepted, and always has to have a variety of explanations to pontificate on. Where every fucker has a mouthpiece, and where motivated grifters can get a spot on a marginal but influential press outlet desperate for engagement. I don't think there are any ideal answers here... Maybe there are some lessons, but they are very hard to unpick in any meaningful sense, and often just lead to further problems. And in the time it takes to properly implement them, the world will have changed again.