Has any world-class pro been able to, for example, play 16th notes at 151bpm on left foot, 16th notes at 156bpm on left foot, 16th notes at 33bpm on right hand and 16th notes at 276bpm on left hand all at the same time, and just loop it over and over continuously for multiple minutes (or hours?) at a time?
To me, that would be ultimate independence. Let's forget about whether it's a 'musical' thing to do and just think of it academically.
It just means you're able to keep 4 separate internal metronomes going simultaneously without relying on any patterns of relationship between them. When there are relationships between two different tempos, playing them together is a lot easier (for example, tempo x is twice as fast as tempo y), but if there is no relationship between the tempos, you cannot rely on one being a 'frame of reference' for the other(s) and you truly have to be able to play them independently.
To me, that would be ultimate independence. Let's forget about whether it's a 'musical' thing to do and just think of it academically.
It just means you're able to keep 4 separate internal metronomes going simultaneously without relying on any patterns of relationship between them. When there are relationships between two different tempos, playing them together is a lot easier (for example, tempo x is twice as fast as tempo y), but if there is no relationship between the tempos, you cannot rely on one being a 'frame of reference' for the other(s) and you truly have to be able to play them independently.