My partner needed help in the OR, and our ethos is that when a fellow surgeon asks for help, you go help. No questions asked.
So I make it to the office ten minutes late. First patient is irate. Despite my multiple apologies and explanations, he wouldn't get over it. (He was really nasty to my staff too, even before the late thing was an issue.)
After a while I told him that I would not be charging him for the visit, but that I did not want to be involved in his care because he was so adversarial. I also offered to refer him to another surgeon.
Once he realized that time/understanding/empathy was a two way street, his demeanor changed. He politely asked to continue our relationship (his issue turned out to be nonsurgical), and he behaved himself through the end of our appt.
Bottom line, we should all do our best to be on time, but also understand that providers are a finite resource. I agree that empathy is key.