I have had my passport checked on a long distance train. The sleepers often have 1 or 2 railway police on them and, on a 12-14 hour journey, it gives them something to do.
For long distance train journeys of course I would carry my passport as I would in all probability also be moving hotels and the new hotel would need to see it.
But for any other short day train trip I would only carry the copy, for all the good reasons given before.