Users normally place their icons using a given, single resolution, so that would only give you one initial saved icon position. You need some heuristic when the user first changes resolution with that icon present on the desktop.
*lifetime of that computer
Icons need arrangements in each combination of monitors, resolutions, and scaling. So that when I'm sitting at my desk in the office I have a consistent experience of icon location. When I'm at home and have different screen layout, I can have a different icon layout suited to that screen layout and everytime I plug the dock in at home I should get the same arrangement that I had yesterday. If there's a new icon that has never been placed in a particular desk setup, drop it anywhere.
Does it change often enough that an absurd like 20s update-time would impact you?
Anyway, the article has plenty of reasons to save more than 1 resolution as "user-defined positions". But not a lot of them, probably 2*n^2 for n monitors is more than enough.