What broke my heart about this scene wasn’t the fact that he was saying the same thing that David Tennant said when he left Doctor Who. In fact, that only occurred to me upon my second viewing.
No, what broke my heart was the fact that this was a frail old man. Sometimes grumpy, sometimes just downright mean, but Doctor Who brought him genuine heart and pleasure.
Children loved him. His granddaughter was proud of him, and his wife knew how much this meant to him. But he was growing old, and he was no longer fit to play such a role.
He was suffering from dementia, and he knew it. And while the realization that you are slowly losing your mind is enough to drive anyone to tears, you have to add to that the fact that his age, his illness, was robbing him of the one thing that had been bringing sunshine into his otherwise gloomy life. He was being forced to let go of the thing that he loved above most other things. I can’t think of anything more painful than that.