In my opinion it seems convenient but illogical to embed orientation/inversion information in an image
Thanks for sharing your opinion, but based on many years of experience with VTK and ITK and several applications that use them, we have come to the conclusion that image geometry is best specified by origin, spacing, direction, and extents. Less than that is very limiting (we have been suffering from missing direction in VTK for very long time) and more than that is not necessary (ITK proved this).
The additional container classes that you propose would make the design much more complicated for additional flexibility that we don’t need.