How usual/unusual was having a skull on your uniform hat at the time nazi officers were doing it?

Assuming the nazis must’ve thought of themselves as the good guys, I’ve always found it almost ridiculous that they walked around with literal skulls showing on their hats, Disney-villain-style.

Would it have been meant like that? Eg. “We’ll wear it so people will fear us and know we mean trouble”. Or would it have been more neutral for people to see skulls and the like at the time? So something more on the line of “We can be scary if you’re the wrong person but otherwise you’re fine”? Did other uniforms across Europe have similar symbols at the time or previously?

Thanks for your replies!