I read the Wiki, but am confused as to why Pro Motion is so good for pixel art if I'm not supposed to use any of the tools. If I can't do that, isn't MS Paint pretty much as good?
If the wiki says that, the wiki is wrong. ProMotion is made specifically for creating 2d game art; the majority of which is still pixel art.
The philosophy behind minimizing tool usage is largely about simplifying your choices.. If your tools place 'accidental' pixels, you have then to concern yourself with cleaning them up. If you use more colors, you have to concern yourself with the shapes of more color regions. If you include more objects, you have to spend more time on composition, Larger canvas.. more time on refining the shape harmonics.
Everything takes more attention, the more of it you include.
That's why it's good to start out as small as you can, with as few colors as you can and a simple style.
For this moon image, it can be reduced to at least 16x16 without losing any of it's moon-ness, and it's perfectly possible to draw it in a mere 2 colors. I recommend it.
Here is an example based on your moon -- in 2,4, and 8 colors respectively, with individual stylistic choices matching the respective limitations.
Joseph: My main criteria for whether I can take a program seriously in it's usefulness for pixeling is, does it allow you to change to next/previous color in the palette easily?
MsPain doesn't. Photoshop AFAIK doesn't.
DeluxePaint does. Grafx2 does. Gimp does. Promotion does. IDraw probably does.
MsPain does have a reasonable bezier tool, but that is about all I can say for it; it's name is well earnt.