Why is the resistance of the circuits input voltage not taken into account when calculating overall resistance of the circuit?
In analyzing circuits you are going to make certain assumptions which simplify the task (in simulation you may use more accurate models in some cases, in others you may use similar simplifications. 

For example, if I am analyzing an amplifier (or simulating in SPICE) I will likely use an ideal voltage source for most of the simulation, maybe all of it. I might add some series complex impedance and/or noise to verify how it behaves as one step. 

Your example of a battery- experience (or a bit of arithmetic) will tell you that the internal leakage of the battery is of no consequence- 50M in parallel with 20 ohms is so close to 20 ohms as to not matter. 

What does matter significantly in your hypothetical case is the internal resistance of the battery  (which is not a constant- it varies with the charge state of the battery, with temperature, and with the recent history of discharge due to 'polarization' effects). The other thing that matters is the open-circuit voltage of the battery, which varies with internal temperature and with charge state. So we might (as a first approximation) think of the battery as 9.0V ideal voltage source with (say) 3\$\Omega\$ in series (FYI, the Circuitlab model defaults to 2 ohms- that resistance will rise as the battery discharges). Either will give a more accurate answer than 9.0V ideal with 50M in parallel (the latter which would have no effect other than to drain the battery). Your 20 ohms in series will mean that the battery terminal voltage will drop to 7.8V and the current will be only 0.39A (using 3 ohms). 

Now, if we are analyzing the battery life with a very light average load, the 50M will be important and we may need to include it to get a good answer. The battery will expend its mA/h from that resistor eventually even if there is no external load applied. But if you have even a 1M resistor load, the 50M will be of little consequence- the variations from battery to battery and resistor tolerances will likely exceed that.