This allows line art to run only once for each modifier stacks, with an option to toggle a specific line art modifier should use cache or re-do their own calculations.
This doesn't really need statistic files because you can just add multiple modifiers and by default the whole modifier stack will only run line art once. There's an Use Cache option on top of line art modifiers (if you have multiple), disable that to have that specific modifier run line art again for maximum flexibility (Chaining and several other options are not separately adjustable when using cache mode).
If need to see cache in action, simply use my 727 test file: https://cloud.blender.org/p/gallery/608da4565f9fe397b1944ba2

