That doesn't make sense - TIM is used to fill the gaps where the copper and silicon don't have direct contact (that's why you use as little of it as possible),

That doesn't make sense - TIM is used to fill the gaps where the copper and silicon don't have direct contact (that's why you use as little of it as possible), not as a heatspreader itself. A direct heatsink-silicon contact will almost always be better for thermal conductivity...