I think it's Rector who gets that note from his mother? Poor guy. I'd like to put him in charge of something. But the person who suggested Charter has a good point. Leliana has Charter and Rector seems to send quite a few reports back from what I recall, Cullen has Knight-Captain(?) Rylen and...I think she's a Knight-Lieutenant Briony-something who both have their own commands and seem to do quite well. So there are already competent people 'waiting in the wings,' so-to-speak. I think that Leliana would want to pick her replacement, but, if I understood the arrangement correctly, Cassandra was to pick one for Cullen if it became necessary.
And while initially I thought Varric would've been great (because I was still on the fence about Leliana), I think he's right in saying he'd be a lousy spymaster because of all the hand-holding and the fretting and the feeling bad about bad things that he'd be doing.
Edit: The Iron Bull is an interesting idea. While I don't think it's a bad one, personally I would prefer promoting an established npc over a companion. As well as the fact that the Iron Bull has a few different outcomes for the end of the game and that might be difficult to marry for the sake of consistency.