They actually don’t. They work fine for a few words then the ink fades out and is basically gone after the fifth or sixth word. I just tried (go ahead and try it yourself, I used just a regular Bic pen). A similar thing occurs when writing on a vertical surface.

Pens also do poorly when cold.

Space pens use a pressurized ink cartridge that works independent of orientation and works when hot or cold. They’re cheap. It’d be dumb to NOT use a space pen on a mission now.

Before the pressurized ink cartridge of the space pen was invented, they used grease pencils.

Actually, the space pen is an example of successful private invention inspired by and then applied to and utilized by NASA.

They don't work well.