This show has essentially two modes when using characters who are supposed to be actual historical figures, one dimensional iconic and there as comic relief (Nero, Churchill, and Elizabeth already in her cameo in The Shakespeare Code), or three dimensional and bonding with the Doctor and the Companion

And if a personality as powerful as Elizabeth Tudor had been allowed three dimensions, she would have taken over the episode, which wouldn't have been a good idea in a special anniversary story supposed to be focused on the Doctor(s). You can only do a Van Gogh episode by giving the historical personality equal weight with the Doctor and Companion.

(Using Elizabeth's mother as I don't have an icon for the lady herself.)