They are band-limited. That's why you get aliasing when taking unfiltered photos above Nyquist without AA filters.

In your example the lower res image would be using most of its bandwidth while the higher res image would be using almost none of its bandwidth.

Images are 2D discrete signals. Everything you know about 1D DSP applies to them.

If some of the edges are infinitely sharp, and you know which ones they are by looking at them, as in my example, then it's using more than all its bandwidth at any resolution.

That's true in the 1D case as well. That requires upsampling with information generation before downsampling. Using priori to guess missing information is a task that will never be finished and is interesting. It isn't necessary for a satisfactory downsampling result.

One interesting complication for a lot of photos is that the bandwidth of the green channel is twice as high as the red and blue channels due to the Bayer filter mosaic.