Jack Kincaid, as a guardian of Earth, is drawn from many different superhero films past. He wears a metal suit strongly resembling Iron Mans, as well as the Batcave from Tim Burton's Batman film.
Schulman cites a bit of Dustin Hoffman in Kramer vs. Kramer, referring to the 1979 divorce story about a workaholic father losing custody of his young child.
Joost takes a break from Tom Hanks' Big home.
The realisation of Jacks isn't that he's a superhero, but that he's a father and a superhero. Much of the film focuses on his relationship with his son, Charlie, who has no clue that his dad is a superhero and feels like his dad abandoned the family for work reasons. (That term has always been a problem, but it's appropriate here, because it literally is a cave), and a live-in bachelor pad, which he could probably practice more.
For a specific reason, the superhero film does show the kids and the Guard facing off against bad guys. The main conflict between Jack and Charlie is. Schulman and Joost wanted to focus on a different conflict than normally seen in superhero films.
Schulman: "They aren't Marvel." Were trying to create a different genre. For us, that meant examining the family dynamics, the father-son bond, and then, if you're very, very clear on it, you'll think, Oh, well, his job is to save the world, but his son wants to save his family.
Secret Headquarters is now available on Paramount Plus.