Hebog
CPS
not to prejudice any case the CPS may or may not have
That's one point of view.
Another is that a police investigation/possible criminal proceedings should not impede the objective of the AAIB which is to make recommendations intended to prevent future accidents and serious incidents - and to issue its final report as soon as it is in a position to do so.
Opinions will inevitably differ about whether priority should be given to improving flight safety or to finding out whether any criminal offences may or may not have been committed.
Inquests
The AAIB does not have to wait until an inquest has been held before publishing its report.
Where there relevant criminal proceedings, Coroners formally open an inquest but are required adjourn it until the conclusion of those proceedings.
In serious/complex cases, the Chief Coroner may decide that an inquest should not be conducted by the "Senior Coroner" for the relevant area but by a serving or retired judge.
eg Hillsborough, London bombings 2005, Jean Charles de Menezes shooting, London bombings 2005, the death of Ian Tomlinson in the City of London.
(The title "Senior Coroner" was invented in 2009 and, in my view, is misleading because he/she may or may not have either the expertise or the experience which the rather grand title suggests.
The process for appointing coroners is, and always has been, curious - to say the least.)