> Lossy or not, the training data provides value.If we ignore the issue of machine learning for now; It's not the job of copyright to prevent people extracting value from a copyrighted work.
If it was, then it would be possible for copyright holders to launch lawsuits that block entities from using the knowledge that was published in copyrighted reference material. Or the rights holder of a cookbook would be able to block people from making the recipe.
We have other sections of law that provide protection along these lines. Patents give their holders a monopoly to extract value from the given invention, a much stronger protection that copyright law. But in exchange Patents are limited to 21 years, much be publicly documented and only certain types of things are covered.
Trade secret laws can be used to protect recipes, formulas and other processes, but only as long as the holder makes reasonable efforts to keep it secret. The owner can't have it both ways, have the IP publicly known and protected by trade secret law.
The only purpose of copyright is to give the holder a monopoly over the reproduction of a work. The definition of reproduction might be quite wide these days: A performance of a work is a reproduction, a cover of a song is a reproduction, distribution is reproduction in the modern age of computers... etc, but the limit of copyright law is reproduction.
Coming back to machine learning, there is a somewhat open question if training counts as a form of reproduction (well, outside of Japan). But we can't use your proposed "extraction of value" metric as a way to decide that.
Personally, I would argue that training a machine learning model is roughly equivalent to a human brain consuming copyrighted works, and should be treated the same in law.
The fact that a machine learning model is (sometimes) capable of recreating a copyrighted work later shouldn't be held against them, as a human brain is also fully capable of recreating copyrighted works from memory. From a legal perspective, recreating a copyrighted work from memory will not save a human from a copyright infringement lawsuit, it's simply not a defence. The copyright infringement happens when the work is recreated.