The demons wore masks so they could protect their eyes. For them, their eyes are their main weakness. It wasn’t shown in detail in the anime, but the demons’ central eyes have plenty of nerve tissues. This makes it harder for them to regenerate those areas. And even if they don’t get fully destroyed, it takes a longer time for them to regenerate those. Meanwhile, wild demons don’t wear masks. It’s probably because they don’t know how to build one, what with being mindless monsters and all.