I'm not sure I'd agree that Dak's issue is with being able to change calls at the line. And I don't think comparing him to Brees in that regard is all that helpful. Brees is, what, 40, and setting all-time records.
Seems to me that Dak's probably is that his accuracy goes to pot when he gets pressure off the edge and we're not doing a good enough job protecting him. Couple that with his (really good) natural tendency to take care of the ball and you get a guy who won't pull the trigger in a lot of situations coupled with a lot of situations where he's now throwing with poor mechanics and accuracy because he's under duress.
When we protected him right, he's a great QB for this offense because he takes care of the ball, protects leads, and can move the chains with his legs. He can make some great throws when his feet are right that can win close games. He's a great leader and a great team guy.
When you don't protect him, though, and when you're getting 2.6 yards/rush in your running game, he's not going to take chances, and he's going to kill drives with poor throws under pressure on 3rd downs.
It's a tough situation to be in. They need to protect him better, and they need to let him run the ball a little bit more.