Some countries require you to bring a copy of a passport on shore but never had anyone ask for it.
In Russia, if you had no visa, you could not leave the ship. Passports are needed to book a cruise ship and you cannot book one without a passport or cruise insurance.
You can always get medical care on shore and claim on insurance. Doctor on board charges an enormous fee but also covered by insurance. My insurance cost 1400 pounds multi trip including USA. Europe cover is much lower priced. Over 70 and premium begins a steep curve upwards.
I know one young man went on a mountain bike in Europe and broke his back. treatment cost and repatriation cost him about 20,000 pounds as he had no insurance for riding a mountain bike. If you were to ride on one of the boat towed plastic bananas etc, you need water sports cover. Most travel cover is just for normal pedestrians/ Moped hire is also not covered by travel insurance if you fall off.
I insure but have never claimed but my premium is high due to joint replacement and Aortic aneurysm.
It should be good to get me home.
Not going to Caribbean again as the danger is illness in the Atlantic on the way back and no chance of any land based treatment as they found in that little ship last week.
To get off the ship and onto land at any European Country, they only look at your ship pass which is the door key. You do get searched on return from land for drugs or firearms etc. I get a good search as my metal joints sets the alarm off.