It’s fair to say that in An Adventure in Space and Time, the film depicting the early years of Doctor Who, the weepiest moments were when it called forward to the subsequent history of Doctor Who — “the winking nods to fan-known futures or characters espousing things said in episodes not yet made,” as Kyle Anderson put it in his review.
Which is to say that An Adventure in Space and Time is borrowing its emotional freight: the tears — the emotional impact — come from what we already know and feel about the subject; what we see on the screen we do not see in isolation. It is because of what Doctor Who will become that we respond to it the way we do, and what we think of Doctor Who may well determine how we respond to An Adventure, or whether we respond to it at all.
It occurs to me that all biopics have this in common: a film profiling a famous or historical person will derive a good deal of its power from our existing impressions of the person or the historical events in which they lived. This could be why so many movies of this sort seem so paint-by-numbers, if the movie’s subject does not personally resonate with you: it is sufficient to tap into that existing vein, because the audience self-selects.
In other words: I like Doctor Who, so I watched An Adventure in Space and Time, and enjoyed it. It’s hard to say what I would have thought of An Adventure if I didn’t like Doctor Who, because I almost certainly would never have bothered to watch it.