What do you consider modern? The "Hero's Journey" coined by Joseph Campbell in 1949 speaks of: "A hero ventures forth from the world of common day."

In the call to adventure: "the hero or protagonist lives in the ordinary world." And this wasn't invented by Campbell. He was the one to break it down, but it can be traced back to mythology.

An "everyman" becoming a hero is about as classic a plot as you can get. Luke was an everyman moisture farmer. There are many other examples in this thread.

Even if you want to narrow it down to real-world plausible situations, there are plenty of action movies where "everyman" characters have to be heroic. Personally, I'd give Indiana Jones the nod before John McClane. After all, McClane isn't truly an everyman. He's a trained police officer who may be off duty, but it's basically his job. Indiana Jones is a professor with realistic flaws ("I don't know. I'm making this up as I go.") who ends up fighting Nazis.

It just makes sense that the protagonist who we're rooting for is kinda like us. It makes us wonder what we'd do in a similar situation. It makes us like the main character more.