Why does Varys want to find Sansa?

[Jô Maltese]

I think Varys may simply try to hold his promise to Ned Stark... And that his care for the children of the realm is genuine:

- his own childhood was probably a nightmare;

- he witnessed the massacre of Rhaegar's infants;

- his last speech to Kevan is coherent to what he tells Eddard in the black cells "children are the first ones to suffer from bad rulers".