Distillation does not reveal the weights, it produces a different network with similar behaviour. Weight space isn't even identifiable: permutation and scaling symmetries mean many weight sets give the same function.

The model also lacks the machinery. No training loop, no gradient descent, nothing to write to.

And a model only sees its own sampled tokens, not the distribution behind them, which are possibly filtered or post-processed. Distillation from that works but is less sample-efficient than soft-label distillation.