Can I not use a simple voltage divider to get the 1.1V?
Sure you can. It's not a good idea, but you certainly can do it.
From the data sheet, the 1.1 volt bus has a range of 1.05 to 1.2 volts. The 1.1 supply drives a number of digital lines whose state (and therefore current requirements) varies wildly, from potentially zero to some max. From page 29 of the data sheet, a maximum of 76 mA seems a reasonable number to design around.
1.05 volts over 76 mA gives a nominal digital load impedance (for high current) of about 14 ohms. To allow a 15% rise when the load is removed requires the Thevenin resistance of the voltage divider be about 1/6 of this value, or about 2 ohms. Then, roughly speaking, the divider will be a 2:1 divider with values of 3 ohms and 6 ohms. Total resistance is 9 ohms.
From this, we can calculate the power dissipated in the divider, and it is about (3.3^2)/9, or about 1 watt.
And that's with no margin. If we restrict the voltage swing on the divider to 1/2 the specified range, the power dissipation goes to 2 watts.
Assuming the specified regulator has an efficiency of 80%, at 1.1 volts out and 76 mA its power dissipation will be about 20 mW.
Plus, of course, the 1.1 volt level will vary by a few millivolts over the current range, rather than a much larger swing.
So, yes, you can use a voltage divider. You'll dissipate something on the order of 100 times as much power, but you certainly can do it.