imresize() Extra Resolution Benefit Limit

Hi, I'm generating highly detailed images at much higher resolution than what will be displayed and/or printed, and I use imresize() with either bilinear or bicubic interpolation to bring down the resolution to displayable/printable resolution in order to get extra details at lower resolution.

My question: is there a 'maximally useful' super resolution, after which the downsampling gains no benefit (2 times or 4 times, for example), or the higher the resolution of the original image, the higher the effect on the downsized image (10 times,100 times more pixels,etc). In more technical terms, since the interpolation kernels only use 2x2 (bilinear) or 4x4(bicubic) pixels, does the resizing algorithm only use these neighboring points and discards the rest, or does it downsample many times, re-using the newly created pixels until the final lower resolution is reached(or some other iterative application).

Thank you very much.