Emily in Edge of Tomorrow and Sicario more than proves that she's great in action roles. She has the athleticism, physique, and acting chops to carry her own action franchise. Matt Damon has Jason Bourne, Tom Cruise has Mission Impossible, Milla Jovovich has Resident Evil, Kate Beckinsale has Underworld, Keanu Reeves has John Wick etc. why not Emily?
It's also such a missed opportunity that she didn't end up playing Black Widow (she was offered the role but had to turn it down) because she's a believable badass spy. Also there's a reason why MCU's Black Widow action scenes in Civil War and Winter Soldier are heavy with the shaky cam, quick cuts, sped up, close ups, and/or off-center framing. This was obviously done to hide the fact that it's a stunt woman doing all of the stunt work and to cover the fact that the actress is not naturally athletic when she is shown doing the easier stunts like running.
Having seen Emily's believably clear action scenes in Sicario and Edge of Tomorrow there's no doubt that she would've portrayed a better Black Widow.
Edit: She's so versatile, she has starred in comedy (The Devil Wears Prada), musical (Into the Woods), drama (Girl on the Train), horror (A Quiet Place), to action (Edge of Tomorrow).