shouldn’t the BSDF model of the material let us roughly estimate the strength the light source?
Yes! However, that would only be true if the exposure of the camera is known since a bright light with a higher exposure might look the same as a dim light with a low exposure, everything else being equal. You could also estimate the size and distance from the subject based on the shadows it casts, but to tie all that together would (I think) take some serious machine learning.
