Sure, you can view an LLM as a lossy compression of its dataset. But people who make the comparison are either trying to imply a fundamental deficiency, a performance ceiling, or trying to link it to information theory. And frankly, I don't see a lot of those "hardcore information theory in application to modern ML" discussions around.
The "fundamental deficiency/performance ceiling" argument I don't buy at all.
We already know that LLMs use high level abstractions to process data - very much unlike traditional compression algorithms. And we already know how to use tricks like RL to teach a model tricks that its dataset doesn't - which is where an awful lot of recent performance improvements is coming from.