I want to just edit it as a black-and-white image, like any normal layer.
Click the Layer Mask on the Layers Panel, then turn off the visibility of the other channels in the Channels Panel by clicking the eye icon next to the [RGB] (or [CMYK]) channel.
You can then highlight the mask channel and edit it like a greyscale image layer.
(This is really what Option/Alt-clicking the mask thumbnail does)
I found the answer; Alt-clicking the layer mask opens it for editing. (This is seriously awful UI design.)