There's nothing wrong with white coats per se. They are a traditional and universally recognised symbol for "doctor"!
It's more a sign of a lab technician these days. The only time I've had to wear a white coat is in pathology or public health.
Our dress code policy was written by our previous head of department and he had a thing about not wanting to look too much like IT, who have sweatshirts with organisation's logo and IT on them, thus it's shirt and tie.
Now the bare below the elbow campaign has come, we sometimes look smarter than the doctors! If anything now a days the traditional symbol for a doctor is a stethoscope draped around their shoulders.