Dutch also has one word for happiness and luck ("geluk"), although in Flanders you can use "chance" to express "luck" specifically (borrowed from French).

In some ways, English allows for more specificity compared to German, but the reverse is also true.

As a native speaker of German I feel often more comfortable to advertise products in English but that is probably because I'm so used to English advertisements and I'm not so exposed to that particular vocabulary in German (or maybe German is too precise to really shine in advertisements). I don't think I could translate an Apple keynote into German and still sounding so 'magical'.

Maybe there are some words you can't translate literally or they don't sound as nice (contrarian: Querdenker, Nonkonformist) still you would miss other awesome things like the German way to combine nouns to infinite length.

Some of smsm42's example do have this property:

"Eigenwert" (eigenvalue): eigen (of (it)self), Wert (value)

"Weltschmerz": Welt (world), Schmerz (pain)

"Poltergeist": poltern (to rumble), Geist (ghost)

English prefers to borrow words from other languages. Curiously, it has borrowed hardly any words from Mandarin Chinese.

Besides that there had been much less contact between English speaking countries and China than to, say, German, French or Spanish speaking countries (at least until the Chinese economy began to boom) there is another reason that I can imagine. Since the Chinese dialects/languages are tonal languages their sound is much more foreign to the ear of people who didn't grew up with a tonal languages. Indeed people who learnt to speak one of the Chinese dialects told me one of the first exercises is learning to even consciously perceive the different tones.

Every child knows poltergeist, from Harry Potter. Every teenager knows angst.

The others are less universal, but I'd expect a university graduate to know them.