I would like to suggest adding an axes_cls parameter to add_subplot()/add_axes(), to support creating axes using custom Axes subclasses -- specifically with the idea of better integrating axes_grid/axisartist into Matplotlib.

Currently, using an axes_grid/axisartist Axes requires a rather unusual sequence of calls, of the form

from mpl_toolkits.<...> import SomeAxesSubclass
ax = SomeAxesSubclass(fig, 111, **kwargs)
fig.add_subplot(ax)  # It's quite rare to call add_subplot() with an Axes instance!

instead, I propose that one can simply write

from mpl_toolkits.<...> import SomeAxesSubclass
ax = fig.add_subplot(1, 1, 1, axes_cls=SomeAxesSubclass, **kwargs)
# or, in the common case (add_subplot defaults to 111):
ax = fig.add_subplot(axes_cls=SomeAxesSubclass, **kwargs)

Note that there is precedence in that plt.figure likewise takes a FigureClass argument for custom figure subclasses. (If we wanted to be consistent we could name the new kwarg AxesClass instead of axes_cls, but... ugh.) Also note that axes_class would conflict with the projection kwarg, because projections (e.g. polar) are also implemented as custom axes subclasses, but that's just how things are: you can't automatically combine a mpl_toolkits subclass with a projection subclass.

See also #17335 (comment).

One side advantage is that this would also make all the explicit Subplot classes (HostAxes vs. SubplotHost, axislines.Subplot vs. axislines.Axes) unnecessary: add_subplot would dynamically create the subclasses, with exactly the same machinery as it does for the normal Axes/Subplot.

I don't think the implementation will be particularly hard; as usual the hardest is deciding whether we want this or not :-)