[machiaweliczny]

Doesn't German work this way?

[mkl]

Not really. "German grammar allows for the construction of long compounded noun phrases which are expressed as one word in written language. Compounding is not really the same as agglutination.": https://www.quora.com/Is-German-considered-a-true-agglutinat...

There are quite a lot of languages that do though: https://en.wikipedia.org/wiki/Agglutinative_language

[gumby]

Not just in written language, although the difference between a “word” and “noun phrase” in spoken language is in the ear of the beholder.

But in a linguistic sense indeed, German is not at all an agglutinative language.

[pault]

English too. Policeman, bathwater, catwalk, headstone, toothbrush, etc.