If you’d like to have a smooth looking censored image you can then blur the mosaic result to have a smooth transition between the censored and original image.
If you simply blur or simply downsample there’s a significant ability to recover data or iterate over data to recover likely inputs. Other posts have discussed deconvolution, but think of a downsample as a hash - you can build a rainbow table of inputs, easily for numbers, with more difficulty for faces. If you have a limited pool of “suspects” this technique can work well. Just as with hashing, you should add a salt to the image before downsampling or blurring to make recovery of the original input more difficult. In this case the “salt” is random noise.