IMHO this is useless. A Cropped sensor, APS-C/Whatever/ is still Full Frame for that sensor. It is only cropped in Comparison To a standard 35mm sensor and or a piece of film. The ratio is still the ratio, 3/2, 4/3, 16/9, Whatever.
What if I always used a 2.25" square camera and then switched to digital with a 3/2 sensor. What is the ratio of that change and why would I want to see it.
The crop ratios you are talking about is to compare lens mm, coverage of the lens for comparison to what you might use on a standard 35mm sensor/film.
It really has nothing to do with you cropping an image after you take the picture.