Should an aircraft logbook stay inside of the airplane, or on the ground with maintenance?
As an aircraft owner in the US I never kept a logbook in the aircraft. I do this for two reasons:
Someone from the FAA can come up and ask to the see the logbook when I am on my way someplace. They can then tie me up for hours while they peruse the logs. And if they find something they do not like ground the aircraft until we get the issue resolve. That would strand me at some airport. If the logbook is at home I can tell them to have their local office make an appointment.
If the log books are in the aircraft they can be stolen when the aircraft is parked. Since the log books are a history of troubles repaired on the plane, service performed, etc, they are the authoritative history of the plane's health. As such the log books represent a significant portion of the value of an aircraft (say 10-15%).