The carriage of personal flying log books, with you on an aircraft when you are operating as a crew member is foolish in the extreme
What if you crash and burn? You wont care, you will probably be dead but the investigators will want to examine your logbook for past experience etc.
Same goes for aircraft logbooks being carried on the same aircraft.
Having stated the above, it would not surprise me of course, if there is a law stating the carriage of logbooks is mandatory.