Are there real-world examples where double stats on rings and trinkets are useful? I have been looking at these numbers from the start of the add-on and in 3 months I have never come across different values. But at the same time, the hints for items with versatility are too wide due to the long hint line.

The only time you would see a difference in value would be if one of the slots puts you into a different stat DR break point than the other slot does.

Its the only way that I could think of to allow you to accurately see what you would be getting when this situation occurs.

It is impossible to make some function that will check the values and, if they are equal, hide the second set?

Impossible? No.
Time consuming to rewrite? Yes