No mod icon in ModMenu

I have no plans to take a dependency on some 3rd party mod.

You don't need to be dependent on ModMenu. You just need to put an icon in src/main/resources/assets/modid/icon.png and add a single line to src/main/resources/fabric.mod.json. If you don't use ModMenu, everything works the same, and no issues arise. If you use ModMenu, you see a mod icon there.