I was given a couple when I started my current position in a large hospital. I only wear them when I walk over to inpatient (cancer floor) rounds about 3/4 of a mile away, and only about half the time when whatever pants I'm wearing either don't have pockets, or don't have pockets that are large enough to accommodate all of the stuff I need to take with me (phone, patient list, cards, pen, handouts, occasionally wallet/car keys). So I basically use it as a fanny pack. Although I have used it as a protective smock before, which is helpful when I don't always have a change of clothes in my gym bag.
When I was on fellowship at a large AMC in the midwest, it was common to wear them in integrated care settings too. Literally everyone there from case managers to nurses to social workers and psychologists wore white coats or scrubs. As a youngish female, you were usually mistaken for a patient's family member (and interrupted or asked to leave during assessments and sessions) if you did not, despite wearing a badge. Overall, I'd say read the environment you're working in and even within that, the context matters. I have certain patients that I know are uncomfortable in medical settings and I'll typically hang up my coat on the hook by the door when I walk into their room.