Most image degradations have global effects. For example, blurring caused by optical limitations of an imaging system has a point-spread function which is (theoretically) infinite in extent: a single point of light gets smeared over the entire image domain. The power spectrum of additive white noise covers the entire frequency domain evenly: there are low, medium and high-frequency components to the noise.
Given these observations, it is reasonable to wonder if local filters are sufficient to restore an image. For the case of additive noise, a strong argument can be made that local filters are sufficient.