These actors all have portrayed multiple, unrelated characters in the Doctor Who universe. Only one of these instances was explained or even referenced*, and I am okay with that. In my house, we call it small island syndrome.
If Moffat wants to explain a connection between the appearance of the twelfth Doctor and Lucius Caecilius Iucundus (and possibly Permanent Secretary John Frobisher), that’s totally cool, I think. But it certainly is not required. In fact, explaining it for Capaldi kind of makes the issues with Freema Agyemen and Nicholas Courtney seem more in need of explanation, as well. And the picture above only shows Doctors, companions, or key actors. There have been another dozen and more supporting actors in multiple roles.
*Romana apparently chooses to look like Princess Astra by intent, but it is not really explained in any way.