1) The terminus of an open (non-conducting) circuit always adopts the full voltage at the source or ground, whichever it leads back to.

2) Two parallel branches of a closed circuit MUST support the same voltage drop, else one or the other will not conduct. It's central to the logic of the NOT gate that the voltage drops of the diodes on both parallel branches are uneven. The resistor above the junction cannot have one voltage drop for one branch and a different voltage drop for the other branch at the same time.

Moreover the voltage drops of diodes are "fixed", unlike a resistor. Adding a resistor to the single diode branch would flexibly even out the voltage drop so that both branches would conduct, so a resistor cannot be added to this branch.

Perhaps these assumptions are inaccurate. If so, please clarify. By the way, if accurate, I could not find any previous All About Circuits topic that explicitly discusses these concepts, including the ones about diodes or parallel circuits.

Don