Here's the crazy thing: I don't think you need a QB that can put the team on it's shoulders for the win; I think you need a PLAYER that you can do that with. Doesn't have to be a QB (and it can even be on defense). What you need is a QB that knows who that is, and whether it's him. Phil Simms knew he never had to be Warren Moon; they had Lawrence Taylor. I think certain QBs get in trouble thinking they're the guy when they're not (that is, to me, why Romo had so many bonehead plays in the crucial moments of games). I think Cousins might be that guy that can't do it, but thinks he can.
I agree with that, but having one sure does help, no?
In the case of Simms, sure, he knew he didn't have to be Warren Moon, but he wasn't capable of being Warren Moon, so playing within himself and not trying to do too much speaks to your point for sure, even if Simms was closer to being Trent Dilfer or Brad Johnson than John Elway or Joe Montana.
With Romo, I have said it for years now that he loses his mind when things get tense. Go listen to him when doing games the last few years. The non-stop slurping of QBs aside, he generally gives good advice and suggestions for most of the game, but when a team is in the 2-minute drill at the end of the game, he inexplicably makes suggestions that are like WTF. And I think that is how he played: very good, sometimes great, for most of the game, but in the crucial moments at the end, his brain went haywire, which is why he'd often make the big mistake when it mattered most. Since I have been watching football (mid 80s), there have been quite a few QBs who scared you when they got the ball down 4 with two minutes left when they were going against your team: Montana, Elway, Marino, Brady, Peyton, Mahomes, etc. Romo was on the other end of the spectrum where you felt pretty confident that he'd find a way NOT to get it done.