It is though. Temperature is an aggregate summary statistic used when the observer doesn't know the details of individual particles. If you did know their position, speed and velocities, you could violate the laws of entropy as Maxwell's thought experiment demonstrated in 1867 https://en.wikipedia.org/wiki/Maxwell%27s_demon

Maxwell's demon is a thought experiment that involves a magical being. It's an interesting thought experiment, and it provides some insights about the relationship between macro states and micro states, but it's not actually a refutation of anything, and it doesn't describe any physically realizable system, even in theory. There is no way to build a physical system that can act as the demon, and so it follows that entropy is not actually dependent on the information actually available to physical systems.

This is obviously visible in the observer-independence of many phenomena linked to temperature. A piece of ice will melt in a large enough bath of hot water regardless of whether you know the microstates of every atom in the bath and the ice crystal.

"large enough" and "bath" is doing a lot of work here. I don't think it's necessarily about size. It's about that size and configuration implying the particle states are difficult to know.

If for example, you had a large size but the states were knowable because they were all correlated, they were following a functionally predictable path, for example all moving away from the ice cube, or all orderly orbiting around the ice cube in a centrifuge such that they didn't quite touch the ice cube, it wouldn't melt.

The ice cube would melt, it would just take longer, heat does transfer through vacuum via radiation. And no, you can't control the positions of the electrons to stop that radiation from happening, it is a quantum effect not something you can control.