Hawkeye has been around the comic world for decades, and along the way he's played key roles in a lot of fantastic stories. He's died and been resurrected, he's taken on the mantle of super ninja Ronin, he's killed the Hulk (in Marvel Comics' recent Civil War II arc), and we've already mentioned Fraction's take on the character. But looking to the world Marvel has built with its connected universe, a lot of those stories wouldn't really work in this setting. Marvel's big-screen universe has slowly diverged from the comics (much like The Walking Dead has changed between mediums over the years), and it makes it harder to tell those stories in a faithful way.
Use Captain America: Civil War as an example. Yes, it pitted hero against here, but it was almost a completely different version of the story than the comics event that inspired it. It was also fantastic, which shows there's no shame in changing these stories for the film world, but it means most potential Hawkeye stories would need some wholesale tweaks to work.
