As per my previous post, torsen/gear type LSDs act as open diffs when one wheel is completely unloaded. In other words, there needs to be grip on both wheels (even if grossly uneven) for it to act as an LSD.
So contrary to your statement, an LSD can and will send all power to the open wheel depending on the type of LSD that it is.
Clutch type LSDs are the ones that act as LSDs at all times



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