The doctors whispery voice seems to be an artistic choice
I honestly thought the actor must have been recovering from throat cancer or something so I looked him up on YT and surprised to find that he has a, still raspy, but overall normal voice.
While not as annoying as women that do that vocal fry thing, his whispery delivery is really starting to grate and I think it will make his acting job harder when he has scenes that call for a normal speaking voice or him having to laugh for example (will he sound like Mutly from "The Whacky Races"?).