Michael,
I believe part of the problem here may be that the connection you refer to, whilst obvious to you seems to be less so to others, myself included.
I was reading your original post with interest, thinking there might me something new I could make use of, and whilst I agree that 1 1/4" is a relatively easy number to deal with and remember, I am really struggling to get my head around how 31.75mm or 31 3/4mm is useful, either as a standard, a multiple, or even to remember.
I was hoping you were going point out some easy number in both metric and imperial, like you did at the beginning 5" = 127mm, both being whole numbers and easy to remember.
Along with many others, I seem to have completely failed to grasp the concept in your original post, and would love a practical example where this co-incidence of units using 1 1/4" or 31.75mm can be used and show benefit over current methods of say multiplying by 25.4.