Recent Large Reasoning Models trained via reinforcement learning exhibit a "natural" alignment with human cognitive costs. However, we show that the prevailing paradigm of reasoning distillation -- training student models to mimic these traces via Supervised Fine-Tuning (SFT) -- fails to transmit this cognitive structure. Testing the "Hán Dān Xué Bù" (Superficial Mimicry) hypothesis across 14 models, we find that distillation induces a "Functional Alignment Collapse": while teacher models mirror human difficulty scaling ($\bar{r}=0.64$), distilled students significantly degrade this alignment ($\bar{r}=0.34$), often underperforming their own pre-distillation baselines ("Negative Transfer"). Our analysis suggests that SFT induces a "Cargo Cult" effect, where students ritualistically replicate the linguistic form of reasoning (verbosity) without internalizing the teacher's dynamic resource allocation policy. Consequently, reasoning distillation decouples computational cost from cognitive demand, revealing that human-like cognition is an emergent property of active reinforcement, not passive imitation.