While all hope seemed lost following the end of Avengers: Infinity War, the post-credits scene gave us all hope when Nick Fury was able to get a message off to Captain Marvel. While this made fans very excited for the upcoming, and now soon to release Captain Marvel movie, it did raise one question. "You're calling her NOW?" It seemed like there had been some times in the past that a hero like Carol Danvers would have been useful, but Samuel L. Jackson says all those other problems the Earth has seen were no big deal compared to this one. According to Jackson...
She said only in emergencies. Other emergencies could be handled by the people who were present. It’s just an alien invasion, that’s something that could be handled. Half the population wasn’t dying and flicking off and doing whatever. We finally have an emergency that I feel warrants her presence. This is unprecedented. How are you gonna fight that? I can’t fight that. If I’m not here, I need to find someone to come here who can handle it. All those people are ineffective. They’re great for normal, everyday world disaster. But intergalactic badass who has all the Infinity Stones needs a bit more.
Clearly, Nick Fury has a very specific definition of "emergency" and even alien invasions and A.I. gone mad doesn't actually qualify. It certainly makes some sense. Fury's plan to create "The Avenger Initiative" comes at a point after the events of Captain Marvel so clearly, Fury isn't looking to call in his new friend at the first sign of something normal humans can't handle. He's planning on using others for those problems.
At the end of Avengers: Infinity War, it doesn't seem that Nick Fury is really clear on exactly what is going on, but he knows that Earth's Mightiest Heroes are dealing with it, and when people start to turn to dust, he knows they've failed. At that point, the only option left is to grab your pager.
Samuel L. Jackson's opinion on why he never called Danvers before isn't the only one that makes sense. Director Anna Boden tells IGN that Fury likely didn't want to reveal her existence to the world unless it was necessary. Her co-director Ryan Fleck says Fury was probably considering pushing the panic button ion the first Avengers, but eventually decided against it.
By the time things escalate to the actual alien invasion, if the Avengers can't do the job, it's probably not going to matter too much.
On the plus side, Fury was right, and the Avengers were able to handle all threats prior to Infinity War. If the Earth had been invaded by aliens, Fury probably would have really wished he'd used that pager.
Expect said pager to play a small role in Captain Marvel, as we'll probably learn where it came from. Assuming it works, we'll see the results of pressing that button when Avengers: Endgame comes out in a couple months.