No, film production is not "agile". On larger productions, it's very much a waterfall process. Everything is planned and costed in advance. There's a thread on here by someone in the industry who describes the process.
As films became more effects-heavy, the process has become even more rigid. As someone said of a Star Wars film, "Three years of pre-production, six months of principal photography, three years of post-production". Some directors, especially ones who came from the stage, have problems with this. For a new stage production, actors are a debugging tool. The director and actors go into an empty theater with a bare stage and work through the script to see how it plays out. Scenes and musical numbers may be added, deleted, or rearranged during this process. There have been film directors who worked that way, including some of the greats.
That process doesn't scale to modern blockbusters. Film planning today looks more like classical cartoon planning - it starts with storyboards, and gradually details are filled in. Nowadays, there's often a "pre-visualization" of the entire production[1], a videogame-quality cartoon with every shot that will be in the final product. That's done before actual production is green-lighted. The link below, from a Paris film school, shows previz and production scenes from some well-known movies side by side. Iron Man looks just like its previz shots, just with higher image quality. Even the camera angles match.
As films became more effects-heavy, the process has become even more rigid. As someone said of a Star Wars film, "Three years of pre-production, six months of principal photography, three years of post-production". Some directors, especially ones who came from the stage, have problems with this. For a new stage production, actors are a debugging tool. The director and actors go into an empty theater with a bare stage and work through the script to see how it plays out. Scenes and musical numbers may be added, deleted, or rearranged during this process. There have been film directors who worked that way, including some of the greats.
That process doesn't scale to modern blockbusters. Film planning today looks more like classical cartoon planning - it starts with storyboards, and gradually details are filled in. Nowadays, there's often a "pre-visualization" of the entire production[1], a videogame-quality cartoon with every shot that will be in the final product. That's done before actual production is green-lighted. The link below, from a Paris film school, shows previz and production scenes from some well-known movies side by side. Iron Man looks just like its previz shots, just with higher image quality. Even the camera angles match.
This is not "agile".
[1] https://www.youtube.com/watch?v=IHHMLyjrn4g