I guess it depends what the circumstances are?
I always carry my MOT/Insurance/Licence when I am on the Island, more out of habit than anything else.
A few years back, I was standing outside the Sefton talking to the Manager at the time, Woody and Bob Mc Millan from Honda, when a Copper walked up and asked me if it was my bike parked up. He then started to give me down the banks over my numberplate, I started laughing as I thought I was being set up by Woody, but by the look on his face it became apparant very quickly that he was serious.
I was given a producer, and was told in no uncertain terms, that if he saw me again before I had produced, he would have my bike taken of me.
When I went to Douglas Police station, the Copper asked me why I was there, when I told him what had happened, he said the Copper who booked me was a total T**T, but if I had not produced, he would have gone out of his way to deal with it.
So although we now live in a digital age, for the sake of a few bits of paper, I still take them with me.