I think things that could be added:

• a close method on Figure that forwards through to the manager like show does
• a get_me_a_working_GUI_backend function that can be exposed (but not auto-called!) in matplotlib.__init__

import matplotlib as mpl
new_figure = mpl.get_me_a_working_figure_factory()
fig = new_figure('a label')
ax_dict = fig.subplots_mosaic('AA\nBC')

See also #14024? I think in any case you need to change show to make such figures showable (unless I'm mistaken, in your PR, as it is, figures can't be shown).

import matplotlib as mpl
new_figure = mpl.get_me_a_working_figure_factory()
fig = new_figure('a label')
ax_dict = fig.subplots_mosaic('AA\nBC')

OK, but why can't this be spelled:

import matplotlib as mpl
fig = mpl.figure()
ax_dict = fig.subplots_mosaic('AA\nBC')

The user doesn't need to know that this factory is spooled up? I appreciate that makes some global state, but in __init__ that could just be: _figure_factory = None until the first call to mpl.figure().

On the default branch fig.show() / fig.canvas.manager.show() works (but assumes you have done %gui qt or are managing the event loop on your own). There is currently a show method on Figure that just forwards to manager.show(). I agree with @ImportanceOfBeingErnest 's comments in #14024 that we should not make Figure.show run the event loop (to keep it closer to the semantics of a GUI framework).

linking to a conversation with @jklymak on gitter: https://gitter.im/matplotlib/matplotlib?at=5f9dc6c02a35440715f8e6a3

The lesson I have learned from working on Matplotlib is that global state is a giant headache as is doing GUI integration. I am very 👍 on us keeping the code to do that for the user, but I am not 100% sure we got everything right so am concerned about always calling that code for the user. I think it is important that we maintain a way for people who want to do their own thing to be sure that they will never have to deal with our (likely still buggy) attempts to "do the right thing" have a way to do that (by not importing the module where we act like an application rather than a library).

There definitely needs to be a way

I don't have the bandwidth to push this across the line for 3.4.

Pushing to 3.6

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