Rationale for commonly occurring DC voltage magnitudes in electronics
The history for these common DC voltages came from the requirements came from the transistor designs in the 50's and 60's with 12V and 5V and major companies using them. 

12V was also  convenient for compatibility to automotive voltages although initially less regulated.  Since lead acid cells were 2V , it was common for higher DC voltages to be multiples of 2V like, Telecom products which today are still based around the subscriber line voltage being 48V  (to 54V ) 

Logic IC designs dictated 5V for DTL in the mid 60's and TTL in the 70's  with CMOS going up to 16V in the mid-70's. But still being slower than TTL , they had to lower the RdsOn of the drivers and keep the voltage limited to 5V in CMOS for the 74HCxxx series for TTL compatibility. They reduced the power consumption and increased the speed again in 74ALCxxx CMOS design for half the RdsON of 74HC series and thus designed for 3.3V max.

Major companies like IBM whose 1st computers used these 3 voltages, which are still used today along with -12V and standby 5V. 

HP desktop computer that I had in '74 was the HP9825 which used a SMPS to create 5V which was efficient for the Silicon on Sapphire CPU, 32 character LED display, and the TTL logic.

Generally reduction in standard and BIOS variable voltages are now all done with SMPS on the MOBO around the CPU.

The rationale is to reduce power consumption by 50% using 1/root(2) or 0.707 but 2/3 of 5V was chosen for 3.3V.

Generally Analog peripherals needed more voltage so the 12V hung around for a long time. Then as HDD's no longer needed it, GPU power hungry cards started to used the 12V more so it is still a major portion of the ATX power distribution.