Showing her dragons would have inevitably resulted in her being humiliated, and possibly losing her dragons.  Just needing to display them is an act of weakness, and the dragons themselves were extremely weak from no food, adding to the humiliation.  Plus I assume that Dany was (rightly) worried that "show us your…

I do think Varys is thinking of the realm, or at least trying to do so (with the assumption that having him as a influential figure is also in the best interest of the realm).  But he tried to make Ned aware of the threat to his family even after Ned had been thrown in prison, and is still defending him to Tyrion…