Am I missing something, or would the police be just as well as to wait until the AAIB has published its report, at which time it will all be in the open anyway?
The AAIB does not make publicly available all the data and evidence that they hold. For example, they don't release the audio tapes from the CVR, nor do they publish all the photos from the crash site, as such data would breach personal privacy laws if published. However, such data could form an important part of a police investigation, hence the police have to apply to the courts to have it released to them by the AAIB.