Some of the standards may have come from the conventions of poker chips. It's my understanding that the heirarchy of chip colors in poker games using non-marked chips was white, red, blue. Sets with 4 colors often used yellow or gold for the next higher denomination. It would seem reasonable for a casino manager (or regulator) to pick white for $1, red for $5, and blue for $20 to correspond to the paper currency value sequence. This seems to have been followed for white and red, but my $20 collection has a minority of blue $20's.

It's never easy to try to reconstruct the thought process behind standards that evolved over many years!