It seems these "morphology"s are were made having a black background as a basis. Once the image is white-on-black, the transformation works. From the documentation:
> It was original developed with binary (pure black and white) images in mind
Negate the colors (so that I have white on black):
convert black-on-white.png -negate white-on-black.png
Then do above transformation from the question. However, I had better results with following morphology:
convert white-on-black.png -morphology Dilate Octagon fat-white-on-black.png
Still, nice to have would be to have it work from different color schemes.