Does no one else agree that the Doctor being immortal would undermine the show?
I enjoy the stories in Doctor Who, not the "powers" that the Doctor and Timelords possess. So long as the stories are interesting and creative, I really do not care that the Doctor has a million regenerations, a sonic screwdriver that can do just about anything, or a time machine so powerful that can churn out enough light to replace the sun for a thousand years and destroy the entire universe.
Personally, I think the Doctor Who approach to writing scripts is better than the approach used by TNG writers where they simply get the science advisor to fill in the X-es in the script:
Picard: We need to do X to get out of this place.
Geordi: How about we X the X so we have enough power to X out of here?
Data: There is not enough X, however we can X the X in 10 hours.
Geordi: Perfect! I'll get started immediately.