> Similar to the no-free-lunch theorem, no lossy compression method is universally better than another,

No lunch theorem only works, because they assume you care about every single value of noise. Nobody does. There's a free lunch to be had, and it's order. You don't care about a single pixel difference between two cat pictures, NFL does.

Lossy compression is precisely where NFL does not apply.

Just similar in theorem style, I try to emphasise that no lossy representation is universally (i.e. for all downstream tasks) better than another.