Isn't this generally addressed by applying a gaussian blur before downsizing? I know this introduces an extra processing step, but I always figured this was necessary.
Practically people think that box averaging is too expensive (pretty much it is like that Gaussian blur but computed on fewer output points.)
[1]: https://www.intel.com/content/dam/develop/external/us/en/doc...
If you shrink 10x in one direction, then the other, then you first turn 100 pixels into 10, before turning 10 pixels into 1. You actually do more work for a non-smoothed shrink, sampling 110 pixels total.
To benefit from doing the dimensions separately, the width of your sample has to be bigger than the shrink factor. The best case is a blur where you're not shrinking at all, and that's where 20:1 actually happens.
If you sampled 10 pixels wide, then shrunk by a factor of 3, you'd have 100 samples per output if you do both dimensions at the same time, and 40 samples per output if you do one dimension at a time.
Two dimensions at the same time need width^2 samples
Two dimensions, one after the other, need width*(shrink_factor + 1) samples