That some sentences are syntactically ambiguous is not a fundamental problem of English syntax. Context and intonation are usually enough to guide hearers in constructing the intended phrase structure (that is, non-ambiguous syntactic structure) of the spoken or written utterance. Such a process is called disambiguation, and we do it all the time. Subconsciously. Instantly.
Besides prepositional phrases being ambiguous between adverbs and noun phrase modifiers, stacking quantifiers (the use of multiple quantifiers) also exhibits syntactic ambiguity.
- Every man loves some woman.
This can be interpreted in two ways, depending on which quantifier ('every' or 'some') is given primary scope. The two interpretations are:
- Some particular woman is such that every man loves her.
- Every man is such that he loves some (potentially different) woman.
Given the unlikelihood of interpretation (2), whenever we encounter (1), we usually hear it as meaning (3).
In the case of prepositional phrases, similar clues also exist to help us hear a particular intended reading.
A final point about German. According to lore, German philosopher and great-grandfather of modern formal semantics Gottlob Frege actually despised ambiguity and wanted to create a perfect language that was completely free of it. This suggests that German isn't as naturally disambiguated as you think.