A LLM is basically the predictor part in a compression algorithm that uses a predictor and stores the error like some audio codecs do. Bellard tried this¹! The model needs to be small (relative to the volume of data being handled) for the compressor to be useful though, you'd squint in disbelief at a de-compressor that weighs hundreds of gigabytes just to decompress a few text files.
¹. https://bellard.org/ts_zip/