Whittaker herself says that playing the Doctor offers a chance to be “the ultimate character:”
“To be asked to play the ultimate character, to get to play pretend in the truest form: This is why I wanted to be an actor in the first place. To be able to play someone who is literally reinvented onscreen, with all the freedoms that brings: What an unbelievable opportunity. And added to that, to be the first woman in that role.”
“We had a strange chat earlier this year where [Chibnall] tricked me into thinking we were talking about Broadchurch. And I started to quiz him about his new job in Wales, and asked him if I could be a baddie! And he quickly diverted the conversation to suggest I should consider auditioning to be the 13th [Doctor],” Whittaker said. “It was the most incredible chat because I asked every question under the sun, and I said I’d take a few weeks to decide whether I was going to audition. He got a phone call within 24 hours. He would’ve got a phone call sooner, but my husband was away and there was a time difference!”
(via)