I feel like you are saying "deterministic", when what you really mean is "predictable". They're
all algorithms, just a bunch of multiplies and adds on the image data really. But the algorithms you don't mind are the ones where you feel you have a good intuitive grasp of what they'll do. The ones that seem eerie and break your sense of indexicality are the ones where 1) you're not sure what it will do, and relatedly 2) seem to introduce a substantial amount of new information, perhaps drawn from some database of how images look generally.
To sum up: Marigold V2 is just as deterministic as Bayer demosaicing. But Marigold has about 20 billion magic numbers in it, thoroughly dwarfing the source image. It feels less like transforming the image with Marigold, and more like steering Marigold with the image. And who knows what's in that thing or how it works...
(note: I see the same confusion often in conversations about LLMs. People call them "nondeterministic", as if that were some new category of software. But, with temp 0, they're no less deterministic than any other pile of floating point math - and nobody complains that fluid simulations aren't deterministic. No, what they are is unpredictable.)