I believe that the curse of dimensionility doesn't apply here as we are optimizing the "universal apppriximator" of the "surface" of the possible real world function.
> Kernel methods owe their name to the use of kernel functions, which enable them to operate in a high-dimensional, implicit feature space without ever computing the coordinates of the data in that space, but rather by simply computing the inner products between the images of all pairs of data in the feature space.
- https://en.wikipedia.org/wiki/Kernel_method
As it relates to this: https://en.wikipedia.org/wiki/Neural_tangent_kernel
To me, this is JFM. Not sure if I'm connecting the dots right either. I just don't know of anything else claiming to solve the curse.