The exact number “24” may be a standard for historical reasons, but a frame rate AROUND 24 is not an arbitrary standard. Higher frame rates require more light so that the image is properly exposed for the 1/(2x frame rate) of a second (assuming a 180-degree shutter angle) that the shutter is open. Doubling the frame rate requires doubling the amount of incident light, so going to 120 fps from 24 requires ~5x more light for a given ISO rating and aperture.
If you think about how light falls off in proportion to the square of its distance from the source—and that generally actors don’t stand in one place, but move through large spaces where they must appear to be lit evenly—you start to see that this is not just a question of “efficient LED lighting.” Shooting at high frame rates requires an enormous amount of light that cannot easily (read: cheaply, quickly, without higher expenses) be brought to bear in a normal production outside of controlled studio conditions.
High-CRI LED lighting is about ten times as efficient as the old film-making standard of incandescent lighting. Inverse square law affects incandescent lighting in exactly the same way, but they still managed to shoot indoor scenes at 24fps using it. Switching incandescent lighting for LED, keeping light locations and power use the same, will make every point about 10 times brighter than it was before. Therefore LED lighting is enough to shoot at about 240fps.
I’m guessing you haven’t worked in the film business, as ‘more efficient’ is not the same as ‘brighter’ in real-world conditions on a film set. LED lighting brings efficiencies in power use, weight, and heat, but nowhere near the quoted figure in terms of raw output due to optical loss, color control, diffusion, among other things.
Unless you are James Cameron shooting Avatar III on a soundstage with (close to) a blank-cheque from the studio, you are still limited in terms of space (the constraints of the location given the size of the light and its supporting stand), time (the time to set up and adjust each light properly, including last-minute adjustments), labor (someone’s got to plug all that in, run the cables, etc.), and cost/availability (you don’t always get the lights you want for a given budget).
Beyond that, you’re also considering aperture and ISO from a creative standpoint; maybe you don’t want to shoot wide open for reasons of image control, and so you may spend your lumen budget on ensuring that a particular scene can be exposed at, say, f/5.6 at ISO 100. Or you may want to spend your lumens on lens filtration, which produces a specific effect but further cuts down the incident light.
In short, no, you do not have 10x light available to spend on frame rate, and for any marginal gains in raw output, most cinematographers are thinking about what creative choices it opens up for the film; I would never burn additional lumens to shoot at 120fps just for the sake of A/V fanboys on the internet, unless the scene requires slow-motion or high-speed capture for postproduction reasons. Technical choices in this industry should always be motivated by the need to solve creative problems effectively, quickly, and within budget.
If you think about how light falls off in proportion to the square of its distance from the source—and that generally actors don’t stand in one place, but move through large spaces where they must appear to be lit evenly—you start to see that this is not just a question of “efficient LED lighting.” Shooting at high frame rates requires an enormous amount of light that cannot easily (read: cheaply, quickly, without higher expenses) be brought to bear in a normal production outside of controlled studio conditions.