Stunt casting is not so much to do with stunt doubles as gimmickry. The best example that I can think of is how Pulp Fiction paved the way for a galaxy of movies whose casting was designed to make you remember that movie.
The Prophecy was filmed within the same time frame as Pulp Fiction (September to November of 1993), hence why they shared three cast members – Christopher Walken (who played Captain Koons), Eric Stoltz (who played Lance) and Amanda Plummer (who played Honey Bunny a.k.a. Yolanda). It was released after Pulp Fiction so as to piggyback on its success.
Miramax had less success, circa 1995, when casting Steve Buscemi (who played the Buddy Holly impersonator) and Walken in Things to Do in Denver When You’re Dead.
In May of 1994, Ving Rhames (who played Marcellus Wallace) was cast in Kiss of Death because Samuel L. Jackson (who played Jules Winfield) was co-starring.
In July, Die Hard with a Vengeance began filming with the particular intention of piggybacking on the success of Pulp Fiction by having Samuel co-star as the black sidekick to Bruce Willis. This is all the more obvious considering that it actually took longer for the threequel to be green-lit than the sequel (this was amusingly because Hudson Hawk was a box office dud). In that same month, Tim Roth (Ringo a.k.a. Pumpkin) and Stoltz were acting in Rob Roy.
Broken Arrow starred John Travolta and featured Frank Whaley in a small role. This was an attempt to remind people about the apartment confrontation between Vince Vega and Brent. It began filming in April, 1995.
The featured image is from Walter Hill’s Last Man Standing. The combination of Willis and Walken was meant to remind audiences of the flashback where Butch Coolidge was being sentimentally lectured by Captain Koons. It began filming in September, 1995. In 1996, Rhames and Buscemi were cast in Con Air. In 1997, Buscemi was cast in Armageddon because of Willis being the star.
In April of 2000, Willis and Jackson reunited for M. Night Shyamalan’s second best film. This was titled Unbreakable. Despite being slightly less profitable than their earlier reunion, it was more acclaimed. Somewhere in that same year, Rosanna Arquette (who played Jody) was cast in Things Behind the Sun because Stoltz was in it.
Such success wasn’t afforded to Basic – a military thriller starring Travolta and Jackson. This began filming in 2001 – several months after the U.S. release of Unbreakable had finished within the same year.
Moonrise Kingdom fared better in 2012 because Wes Anderson necessitated Willis and Harvey Keitel (who played Winston Wolfe) to be cast in 2011. Pulp Fiction is a national institution, so people were bound to pick up on the connection.
In 2008, a similar connection didn’t escape Quentin Tarantino when he decided to cast Keitel and Jackson in Inglourious Basterds.