Finding a Good Estimate for Amount of Time Computers Spend Sorting Lists of What Lengths?
There is no comparison based sorting algorithm faster than O(n log n). So this is all theory.
There are plenty of situations where sorting an array takes O(n) time. These are special cases, but happen a lot. For example a sorted array. Or a sorted array with few elements changed. And there are cases where sorting the whole array isn’t needed. Like if I see my address book on the screen, apparently sorted - but only the bits that I’m looking up are sorted.
Log n isn’t very large, so O(n) doesn’t mean it’s faster than say Quicksort for anything that is small enough to sort.
Server farms rarely sort. Databases are indexed, and indexes are updated, no sorting needed.
The effect on society would be zero. Some people would be able to handle their computational needs for slightly less money, that’s all the difference.