Do Battery Powered devices require bulk cap at power input?
The large input capacitor is required for battery operation because of the high pulse current drawn by the boost convertor.

With reference to the datasheet for the TPS61099x you can see that the cutoff current will be between 0.8A and 1.25A. 

 

Your AAA batteries are extremely unlikely to supply even the minimum of 0.8A when fresh.

Even a fresh Alkaline E92  is likely to see a terminal voltage drop close to 0.2V worst case. As the batteries discharge this will obviously get worse.   

The large capacitor allows the battery to recharge it during the switcher off time, and the majority of the on pulse current then comes from the capacitor. You need a really good quality low ESR cap to ensure that it can provide the high pulse current during the on time.