With tiny mA current the diode would have a linear behavior where delta I in current consumption would translate to delta V in voltage drop. This behavior is undesired since the uP is expecting a constant voltage behavior instead.
Nothing in the above statement is correct.
Diodes have an exponential current/voltage relationship.
The uP does not expect constant voltage, and as stated, can run from about 1.8 - 5.5 V.