I will be happy to retire my student coat that I've worn constantly over the past two years. The sleeves have permanent rings of grime around the wrists, and there are stains from chemicals, food, and um, patients, that just won't come out. FYI- Student coats are shorter in length. If your healthcare provider is wearing a coat that is the length of a regular blazer, than you're probably being seen by either a nurse or a student. If the coat extends to the knees or below, then you're being seen by a resident doctor/attending, or in some places, a nurse practitioner.
Personally, I don't enjoy wearing a white coat. For one thing, I'm pretty klutzy. Also, none of my own doctors have ever worn them. The only people I associate with a long, white coat are butchers. I don't think that is exactly what my profession was going for, but I can't help but smirk when I see the white coats coming down the hall.