Summary
Discourage or deprecate
Axes.invert_xaxis() / Axes.invert_yaxis(). Use ax.xaxis.set_inverted(bool) instead.
Axes.xaxis_inverted() / Axes.yaxis_inverted(). Use ax.xaxis.get_inverted() instead.
These are simple and rare enough so that we do not need to lift the API from the Axis to the Axes.
I'm still not decided whether we should only discourage or deprecate. - It's the usual trade-off between backward-compatibility and making the API simpler / less redundant.