Harry Morgan, though he's dead throughout the entire series, is a pretty important character.
I also would have put on Randy Marsh, one of the greatest character in television history. Up there with Homer Simpson. Though you might also have to accept Randy McCormack, Gerald Broflowski, and Mrs. Cartman/Mr. Tenorman since the clues only specify the show and not the family.
Although arguably he does have a point in that 5 years later, per imdb it is still at the top. (https://thestacker.com/stories/980/100-best-tv-shows-all-time#101) Don't really think the older shows are well represented on there so may be skewed towards Breaking Bad.
I also would have put on Randy Marsh, one of the greatest character in television history. Up there with Homer Simpson. Though you might also have to accept Randy McCormack, Gerald Broflowski, and Mrs. Cartman/Mr. Tenorman since the clues only specify the show and not the family.