Tom Bakers casting in “Day of The Doctor” was brilliant.
The obvious thing was they had to bring in a classic series Doctor and give him something to do. Focusing more on the modern era is fine, but for the Fiftieth Anniversary, they really had to do something to call back to the classic era- and as amazing as it was, the Thirteen Doctor stunt I don’t think was enough. I don’t agree with Colin Baker that they all should have had substantive roles- the run time alone of such an episode would have required a hideously large budget if it was to be done to any real quality. I do like an idea I saw that in the Thirteen Doctors moment, they should have had new dialogue recorded, but much more than that would have been difficult at best with realistic budgets.
Tom was the best choice, easily. For one, he served in the role longer than others in terms of time on the TV show. 7 years active in the role- this makes him highly recognizable as a symbol of the show. A few fans promote alternate metrics, usually leading to McGann or McCoy getting the longest serving spot, but Tom Baker is nearly always given that honor.
Second, he’s the earliest surviving former Doctor. If Hartnell, Troughton, or Pertwee were still around, you could argue one of them should have been pulled in, but they aren’t.
Third- storyline. The Time War and the implications thereof have been major elements of the revived series. “Day of The Doctor” actually showed some of it, the end. But the beginning? From the Daleks point of view, this occurred when the Time Lords sent the Fourth Doctor back in time to avert the creation of the Daleks, or failing that, to make them less dangerous. Bringing in Tom Baker ties “Genesis of the Daleks”, where the war started, to “Day of The Doctor”, where it ended. A major part of the classic series tied to a major part of the revived series, really showing that it’s not two shows- it’s all one show that just took an unusually long break between seasons.
Both stories also included a moral quandary of when, if ever, genocide can be justified.
Given the difficulties of properly including more past Doctors than they did, Tom Baker was, by far, the best choice for a classic Doctor.