Powering 1.8V-3.6V chip from 3xAA batteries

What am I missing?

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Uhmm, the complete set of requirements

This is just a complete guess since the power requirements are not fully provided (i.e. voltage required for motor, and voltage required for transceiver). But my guess is that +3V may not be enough for the motor; but this is really part of the big mistery behind the need...
-> "power a chip with 1.8V-3.6V operating voltage from 3xAA batteries"
-> "2.6V to take a full advantage of available battery capacity"
-> "the closer the voltage is to 3.6V, the better"

But then again, it's all a big guess based on the requirements as provided - but Slowmo does know the real requirements, and he is happy with the powering from MCU; so I think that's good enough (unless he so desires to share all the applicable information which is required to provide more accurate answers and eliminate the guessing).

As the chip is an RF module that needs to transmit having 3 cells and a fixed 3.3v supply will give better all round performance over the battery life than using 2 cells and running the RF chip from 3.2v to say 2.2v over the battery life.

"power a chip with 1.8V-3.6V operating voltage from 3xAA batteries

I suspose you might get a little more power out of the transmitter running at the higher voltage at end of life. But the batteries are gone at .9 volts (1.8 for 2) anyway.
The first time the motor goes on it will probably be all over.
Just seems like a lot of "stuff" for the time that might be gained.
In any case any active componets will make it worse.
The diodes and the micro pin is probably best since it must be on anyway.

Yeah, good point Ronv. I was working with the assumption that the OP wanted a fixed voltage for the best possible operation, but as you said if the RF module is specced for 1.8-3.6v then for most apps you could just use two 1.5v cells.

Personally I'd go for 3 cells and a LDO 3.3v regulator, they are tiny and only cost a few cents. I think a diode would be a poor second choice to a LDO reg.