As a young man I travelled a lot (US only twice, Canada once) in democracies and authoritarian regimes and quickly took the habit of always having some sort of paper on me (passport, copy of the visa and passport, city/tax registration...) depending on the place.
I was controlled countless times, I thought at the time I didn't stand out much but I probably did. I was always unlikely to be detained, but vehicle / luggage searches, questions etc can be a huge waste of time so better show some paperwork that will cut the questioning short and not risk missing your bus/flight/train/meeting etc. It sometimes even helped to get into nightclubs...