The link you provide in the question already mentions one reason for using length-normalization: to avoid having high term-frequency counts in document vectors. This affects document ranking considerably. A direct application of this is, of course, query-based document retrieval.
There are other algorithm-specific applications as well. For example, if you want to cluster documents using cosine similarity between the vectors: simple clustering algorithms such as k-means may not converge unless the vectors are all on a sphere, i.e. all vectors have the same length.