On my wrist? No.
Touring, I wear long pants or shorts that have zippered pockets. I have a very minimalist wallet with a small amount of cash, health care insurance information, some cards with my name & address & phone, a credit card or two, maybe a debit card and a photo ID. If I am staying in any Hostels, I also carry my HI membership card and I might carry any cards I need for motel discounts (in USA I carry my AARP card).
In USA, when you buy a passport they ask if you want a book or card or both. The book is the one that virtually everybody gets. In addition to the book I also got the card to use as a backup photo ID. For foreign travel teh passport card is quite limited, can only be used for travel on land or on water, not in air. And it only works with Canada, Mexico and some Caribbean countries. But, it is a US Govt issued photo ID, I usually carry that in my touring bike wallet. Then if I lose my wallet, my drivers license is not lost. I did use that passport card when I rode my bike from USA to Canada and back to USA, it was easier to carry than the passport book.
Some of my friends that have medical issues wear one on their wrist at all times when on a bike, those IDs list their medical conditions or meds or other contact info.
Several years ago I lost my wallet in an airport. My drivers license was in my pocket, not in my wallet at that time so that was not lost. But, the concept of trying to get on an airplane without a photo ID scared me enough that I decided I wanted a backup photo ID card, so when I got my passport later I also got the passport card to have as a backup photo ID.