Most people I have met recently while traveling (including one from Germany) who I have added on Facebook use their real first name and a fake last name.
Why would it be a mistake since it is a pretty common use pattern despite the rules Facebook tries to impose?
Because "pretty common use pattern" should not be the bar for what is allowed on facebook. To give you another example: in India, it is very common to use a picture of your favorite Bollywood actor as your profile picture on social media. Should this be permitted by facebook just because it is a common pattern in India? In my opinion it shouldn't be permitted because it hurts the core of facebook: people using real identities to connect with one another.
I can also flip your argument and say that why do people who use fake names want to impose themselves on Facebook? They could just as well abide by Facebook's guidelines or just not use it.
Why would it be a mistake since it is a pretty common use pattern despite the rules Facebook tries to impose?