[amatecha]

That's not exactly the aim of lossy compression. Its aim is to reduce data size while introducing as little discernible effect as realistically possible. That usually means optimizing the algorithm such that most of the loss is indiscernible to us, such as in a darkest regions of an image, or the extremely high frequencies in audio -- both areas we don't perceive with too much granularity. Something like spread-spectrum phase distortion may survive compression just fine but still be indiscernible to us. The two are not mutually exclusive.

[AnthonyMouse]

Suppose you could encode 0.2 bits per second of watermark in a recording without humans being able to discern it. Suppose the compression algorithm did the same thing to encode additional information which is part of the recording, allowing it to achieve higher quality at the same bitrate or the same quality at a lower bitrate.

It's information theory. Either you can encode additional information without impacting the result, in which case the compression algorithm could use it to be more efficient, or you can't. TANSTAAFL.

[Dylan16807]

Audio compression algorithms are not trying to be 99.9999999% efficient.

[wizzwizz4]

And complexity theory says we can't reach the information theoretical limits with generic algorithms.

[AnthonyMouse]

If there is a known way to cram more data into the same space, compression algorithms are going to want to use it, or something like it which makes use of the same space. Even minor improvements in compression algorithms are extremely valuable at the scale of the internet.