Why is the transfer function of this non-inverting low-pass filter wrong?
The transfer function of the non-inverting circuit (which is no lowpass) is not correct. There is a simple math error.

The correct expression is:

Vout/Vin=1+ (R1/R2)*[1/(1+sR1C1)]

Hence, for s approaching infinity, the transfer function is approaching "1" (and not zero).