Why is Capacitance Effect Modeled as Admittance Branch and Not as Series Impedance in Transmission Line Circuits?
Because the capacitance models electric field between the signal and return conductors. 

And the electric field in a capacitor is directed from one plate to the other. Therefore in our model, one plate of the capacitor must be connected to the signal wire and the other to the return wire.

An obvious way to think about why the capacitor isn't in series with the signal wire: What is the behavior of a capacitor at low frequency? What is the behavior of a transmission line at low frequency?