The first time this concerned me on an apartment shop, I watched as the leasing consultant placed my license on the desk where we had been sitting in the commons area of the office. There were tenants and a construction crew sitting around, watching TV and using wifi. Before going on our tour, I asked the consultant to find a more secure place to leave my license. She was almost speechless, never having given it a second thought. She told me it would be fine, and I quietly objected again.
I watched as she took my license into a private office. She put my license in a desk drawer, then got keys from her purse, which was in the private office. She locked the office door, bringing her keys with her. After touring, before returning to the office, she apologized for not being more careful with my information, and explained that although she had followed regulations, she could see its weakness.
I digress, but leasing consultants and real estate agents take a chance with every stranger to whom they show properties. Storing a prospective renter's license is a reasonable precaution.
We got back to the office, the consultant unlocked her private office, and returned my license to me. Canada, I cannot be 100% positive that someone, while I was touring, did not have the means to get in the locked office, find my license and make note of my name and address. If there's a risk, I weigh it. I'm a reasonable person who takes reasonable precautions.