Impedance looking into a short coax test lead. What is it?

It is certainly not intuitively obvious to me why the capacitance looking into a coax 50ohm test lead is not factored into account when terminated in the characteristic impedance Zo.

Below shows my confusion.

Why in the case of  the model in Figure 1 would I take the capacitance of the coax into account? (about 30pf per foot) when I terminate in a high impedance? Yet when I terminate the coax in a 50ohm load in the model in  Figure 2 I do not see the capacitance? In other words the model in Figure 3 is incorrect.

Even at a frequency of 2MHz the calculated impedance Zin in Figure 1 is 664ohms magnitude, of course with some phase shift. This means that the capacitive effect of the 3ft coax connecting cable is significant.

Some study of transmission lines is needed to reveal the answer.