Serial idafa expresses nested relationships. Consider:
بَابُ بَيْتِ أُسْتَاذِ الطَّالِبِ
The door of the house of the student's teacher.
The expression is intelligible. Difficulty appears when a very long chain obscures which possession or relationship is most relevant.
Unpack it from the deepest dependent outward: student → teacher → house → door. A chain is not defective merely for having several links if each one is needed and reasonably clear.