[LegionMammal978]

For one, it doesn't obey the transitive property like a truly lossless process should: unless it settles into a fixed point, a perceptually lossless copy of a copy of a copy, etc., will eventually become perceptually different. E.g., screenshot-of-screenshot chains, each of which visually resembles the previous one, but which altogether make the original content unreadable.

[pizza]

Perceptual closure under repeated iterations is just a stronger form of perceptual losslessness, then, after k generations instead of the usual k=1. What you’re describing is called generation loss, and there are in fact perceptually lossy image codecs that have essentially no generation loss; jpeg xl is one https://m.youtube.com/watch?v=FtSWpw7zNkI