Hi,
I have thoroughly tried to get exactly what you have, recreated my version from scratch.
Yes. If done exactly as you have done, which let me say is not "correct" or optimal, the effect of Round Edges gets lost.
The issue here is the use of FrontBack map, specifically having its back color set to Black. If you change black to pure white, you will see Round Edges with Precise mode working correctly.
Apparently Round Edges, especially with Precise mode and when used with FrontBack map, are sensitive to this color changes.
But the main issue here is the not optimal set up of model and/or material.
The box in attached scene has thickness, so there is no need to use FrontBack map. Moreover: if you use FrontBack map, any face which is seen from "behind" has the Back color and does not take into account the Front color otherwise seen from the other side.
I attach renders here to you can understand better.
This is not a bug clearly. You just complicated the material setup I think.
The solution in your case is to simply not use FrontBack map for Opacity, and everything should work fine.
You can find the simple scene I created attached as well.
Hope this helps.