It's a bit more complicated than that: when I receive cash euros, I don't have to worry about how they were previously used. But if you know the money comes from something illegal, you shouldn't get involved.
How do you know if cash euro bills you are using are not secretly marked by government for tracking money flow?
This was used many times in history in different countries with UV ink markings, but more likely they are using some different tech this days.
I even saw several websites and apps for tracking euro bills.