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Why is inverse of a transfer function not really a correct way to think while doing circuit analysis?

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When we try to predict the circuit behaviour using transfer function, everything works fine in forward direction (Vin to Vout).

But if we try to predict the circuit behaviour in reverse direction (Vout to Vin) assuming the transfer function would be inverse of the forward direction, why do we fail miserably?

I get it practically, but why the inverse is not valid theoretically? Is it because the assumptions involved while deriving forward Transfer function (say, no output loading) is not valid when Vin, Vout terminals change?

Eg1: LC low pass filter

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The inverse transfer function predicts the high frequency components will be amplified, which is not the case!

But if I remove C, it becomes bidirectionally valid.

Eg2: Simple resistive voltage divider


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