Why would there need to be a voltage doubler if the output is far below the lowest allowed input?
OK. I'll try to explain.
Here's a basic SMPS block diagram:
Consider the transformer. It is a fixed ratio primary to secondary and doubling or halving the primary voltage will result in the secondary voltage also doubling or halving.
The output voltage is tightly regulated within a small range using PWM control of the primary side switcher MOSFET/TR. The input rectifier, input filter caps, switching transistor/FETs and transformer need to be optimized for the highest line voltage it will see. Let's say 230V AC. Those caps would need to be 400V caps and rather expensive.
In the US, with only half the line voltage (120V) the transformer being a fixed ratio, will output half the secondary voltage. No matter how much you width modulate that half height primary voltage, the average secondary voltage after filtering will not be even close to your target regulated voltage. The primary side switcher current would also double and be outside the overcurrent range of the controller.
So, what do you do? Do you design SMPS supplies for 110-120V and another for 220-240V? You could, but that's extra SKUs and expense. Each will need dedicated transformers, each with completely different primary/secondary windings and gauges. Each rectifier and primary filter bank will be different- one will have lower voltage higher capacitance and the other higher voltage, lower capacitance. The controller IC will also be different.
Or do you take advantage of a neat little trick?
The voltage doubler. Design all the SMPSs to work on 230V and use low cost primary 200V capacitors wired in series. When presented with half the primary voltage in the US, switch in a primary side voltage doubler. The transformer will always see essentially the same primary voltage and hence the secondary will be within regulation range of PWM controller driving the switcher. The secondary side caps can stay the same values. The current flow in the transformer doesn't change so it can stay the same.
Voltage doubler:
Here is the relay switched voltage doubler implementation in the NAD M-22 amplifier. The SMPS itself, then sees approximately 310-340V DC regardless of where it is used in the world. Minimum losses all round.