I think it would be a great little addition to the “mirror” toolset if it had the option to add and/or reposition geometry in an asymmetrical way (in one or all axes). This would come in handy especially for organic modeling (bilateral symmetry is not perfectly symmetrical)
(“Reset Symmetry” would work only on selected vertices)
My two cents.
Why not just add a displace modifier after mirror modifier?
Asymmetry doesn’t seem to fit at all within the context of the mirror modifier.
It’s not the same thing
In that same regard, why not just model one half of a character, then duplicate it, join it with the original half, remove double vertices, and get rid of the mirror modifier… that was the workflow about 4 years ago.
I think it fits very well, look at it this way: when you move one vertex/edge/face the mirrored vertices move to a slightly different position (within a certain range), just like in real life where no half is an exact mirror of the other (and that IS the core of my suggestion), thus breaking instantly the dreadful CG symmetry (i.e. head modeling). If you don’t like it later, you can reset all or just part of the geometry to its original mirrored state.