Why are most consumer electronics power supply boards single sided and made of FR2 (Phenolic resin)?
Cost. The FR2 will be a bit cheaper than glass fibre boards and may be a little easier to machine meaning less tooling cost. Single-sided board will be cheaper than double-sided due to reduced copper cost and processing steps.
Figure 1. XT PC Power Supply PCB - Component Side. Source.
Figure 2. XT PC Power Supply PCB - Solder Side. Source.
Note that some of the traces are rather circuitous to avoid crossover connections on the other side of the board.
Can anyone explain why power supply boards are designed as such?
The circuits aren't so complex and the board can be laid out without the need for wire jumper links. There are none visible in Figure 1.
My guess is that this board mostly contains through hole components, and is easier to wave solder when laid out on a single side.
Double-sided boards are generally wave-soldered in the same way. The traces on top facilitate jumping over other traces and the through hole vias connect the the two layers.
Since FR4 is used for multilayer boards/through hole plating and vias, it is cheaper to lay the power supply out on this type of board.
Yes. You could get a feel for the cost saving by trying to price, say, 1000 PCBs on one of the online PCB manufacturing companies.