The system I work on saves the received data, compresses it and stores it in the clowd. When some data is needed, the files have to be decompressed to be useful. While the files are not really large, this is a use case where decompression speed can affect a system responsiveness, and, with many users, can reduce the overall usage of hardware resources.
Also, I believe there's an effect on compressed communication in the web (gzip header in http requests). Also very small, but can be significant with many requests and heavy content, and also may affect battery performance.
Funny thing is, until you asked that question and I decided to answer, I never thought it was useful