That would mean the speculation would go on for ever. If the killer isn't revealed, the Beales will have no peace and the ongoing investigation will keep recurring, even when we, the viewers, know the answer. I can't see that happening, it would quickly get very boring.
On the other hand, of course, to counter that, it may be that after the killer is revealed to the viewers, the investigation won't be mentioned again even though as far as the residents go the killer hasn't been found which would just be totally unrealistic.