But one cannot actually set it to a value of None from the rcfile (https://github.com/matplotlib/matplotlib/blob/v2.2.2/lib/matplotlib/rcsetup.py#L151).

So in practice, the only change removing that entry does is to replace a specific deprecation message ("axes.hold is deprecated, will be removed in 3.0") by a generic unknown-key message ("Bad key "axes.hold"").

But the rc parser will pass the string "None", not the None object. Manually adding such an entry in your rc file confirms that behavior.

One may want to restore the suppression behavior somehow (but that's a separate issue), but right now the only point is to trigger a deprecation message on get and set (and when doing rcParams["blah"] = None directly).
Anyways, you know very well what I think of all this (with python syntax, you could actually pass None in, yada yada); that's not particularly relevant for this PR so let's not derail it.

As pointed out in #10939 I would expect there to be a way to get rid of the "frame", i.e. the figure's background patch entirely.
As it stands, one may only turn it transparent. So frameon does have a reason to exist, namely to remove the figure patch from the created figure. (This is relevant for pdf or svg output where depending on frameon a rectangle or no rectangle should be created in the output file.)

Why does a transparent rectangle in the output file bother you?
Would fig.patch.set_visible(False) work? (Yes, it's an API separate of savefig. But as I argued elsewhere, we shouldn't replicate the entire figure manipulation API in the form of kwargs to savefig.)

There are several reasons not wanting a background at all. Let's simply say transparency is unfortunately not handled well in every program you might use your figure with afterwards.

Indeed,

plt.savefig("test.png")
plt.gcf().patch.set_visible(False)
plt.savefig("test.svg")

gives the expected result.

But that is somehow inconsistent. If the figure patch is the object to manipulate for the saved figure's background appearance, one would expect that to be the case in general, not only for set_visible.

I.e. the following does not produce a green background,

plt.gcf().set_facecolor("palegreen")
plt.savefig("test.png")
plt.savefig("test.svg")

That's because savefig overrides facecolor and that's exactly why I proposed #10023.
Perhaps at least (in #10023) we can kill facecolor and edgecolor, and leave the discussion for transparent (which does not directly map to a single property) for later?

Not sure I'm following here, but there sure are reasons to let the saved background be different from the one shown on screen, and to do this within the savefig. (Arguments are given precisely in #10023) The full API is there, it's just not implemented correctly for frameon.

One could of course make that more consistent, in the sense of savefig(..., **kwargs) where **kwargs are passed on to the figure patch of the saved figure. So frameon will become visible and transparent will need to be set via facecolor=(1,1,1,0).

I'd rather have the API proposed in #10023 (comment). Let's move the discussion there?
Note that transparent also modifies the axes' facecolors.

Let's simply say transparency is unfortunately not handled well in every program you might use your figure with afterwards.

Do you have a specific example in mind?

Going to merge this, but am open to reverting if we get much push back on this after it is released. I think running this through controlling the color / transparency of the patch directly is clearer than an independent flag.