Shadows are computationally expensive to generate. First the object has to be rendered to a buffer, and then the buffer blurred, and then the blurred buffer, object and background composited together.
Having many shadows on an object makes this path much longer. I can imagine adding this to a page could easily run out of GPU RAM and end up having to discard buffers which later need to be re-rendered.
End result:. Hot slow phone.
I'd like to at least see a benchmark of this effect before suggesting multiple box shadows.