From my readings, this was cultural to the Royal Navy of the time, probably since the looooong blockades and cruises of the earlier wars with the French. Ships would spend weeks or months sailing back and forth off of Brest or Toulon with little to no contact with shore except for the occasional resupply ship bringing letters and newspapers.

So, sailors would organize plays and skits as you said, concerts, athletic competitions, etc.

Even so, if you read the resources and the ship's logs they reference, there was a LOT of petty crime, crimes of passion like assaults, murders, etc during those blockades.

Enough so that it was notable even in the height of the unwilling drafts of any man with a pulse that strayed close enough to the water.