As people keep pointing out, Minfilia's strength doesn't lie in any physical ability. She's not a fighter, and unless she decides to pick up a combat skill, people need to stop bringing that up as an issue. Minfilia's only responsibilities are managing the Scions' internal affairs and public relations. Everything the Scions need, she makes sure they get (including access to retainers). She makes the decisions regarding everyone's assignments and missions, and when there's a problem, she's the one who looks for a solution and seeks out others if she herself doesn't have the answer. She's also your support and confidant. Also important to remember is that people like her handle all the background stuff that makes the Scions into a relevant organization: paperwork, logistics, finances, reports, resources. Those are all the things that she and the other Scions handle for you, so literally all you have to do is go out and kill the bad guy.
Minfilia is to the Crystal Braves what Nanamo is to Ul'dah: literally just a figurehead with very little power. In the case of the Braves though, Minfilia was literally just a name on a piece of paper so that people would support Alphinaud who, let's face it, is pretty much an unknown in Eorzea regardless of his relation to Louisoix. Alphinaud handled everything about the Braves on his own, with Minfilia just being there to offer him her personal support more than anything else.
As a huge Thancred fan, I really don't see how him being a pretty normal and fallible guy makes him angsty. His mentor died five years ago and was a man he really looked up to, and a bunch of people he's closely worked with before (and who are also the men of Raubahn, a man he both respects and works with) died in an assignment that he was a part of. I'd say those are pretty good reasons to have feels. Add that to his determination that he should be protecting the others in Louisoix's absence and his feeling that he's failing on that front, and it's pretty normal that he'd have an emotional breakdown. Apart from that, look at Thancred's general interactions both inside and outside of quests post the 2.0 endgame: whenever you see him, he's either carefree or joking around with the others, or having adventures with several of his lady friends. That's hardly the mark of an angsty person.
As for Minfilia, see my above comment in the same reply. Also, don't misuse the term Mary Sue, it only applies to author-created characters in fanfics.