[tritical]

Yes, your are correct that when averaging pixel values the difference between 1.) averaging the gamma corrected values directly and 2.) undoing gamma correction, averaging the linear values, and then redoing the gamma correction will be greatest when the values to be averaged are very far apart... and 1 will always result in a smaller final value than 2 (assuming the applied gamma correction factor is < 1.0). However, that is not interpolation. For example if I am given y=1.0 at x=0.0 and y=0.0 and x=1.0, and am asked to give a value for y at x=0.5, without any other knowledge about the function there is no reason to believe that averaging y at x=0.0 and x=1.0 will be anywhere close to the correct value at x=0.5. Now if I know that y is piecewise linear that is another matter. However, I would argue that most images - especially edge areas - are much closer to piecewise constant than piecewise linear... i.e. when you have two neighboring pixels that are very different, rarely in the original continuous (infinite resolution) image would the value directly between them be exactly half the luminance.

Also in my ramp example the difference between neighboring function values (that are linear after gamma correction) could be made infinitely large, resulting in as large a difference as you want. That point was only to say that the accuracy of interpolation will be limited by how well the model you use for interpolation fits the underlying data.

Actually, I did a quick test using the training data for nnedi (primarily directional edges and complex textures) and linear interpolation (so the goal is to predict the pixel value at (x,y) given (x,y+1) and (x,y-1)). Linear interpolation on the linear values (undo gamma correction, interpolate, redo gamma) vs linear interpolation on the gamma corrected values did not result in any significant reduction in absolute error or squared error - both in gamma corrected and linear value space. The same for cubic interpolation.