One case where bitplanes could be faster was high-res bitmapped text. As long as your text was monochrome (all in one bitplane), you could write an 8 pixel wide character with one byte. This was a big deal when it came to scrolling a screen full of bitmapped text.
The early Amigas had a memory bandwidth of ~7MB/s, and the chip RAM bandwidth was shared with the custom chips... Anything that'd reduce needed memory transfers was a big deal.
Fun fact! The Amiga Workbench is 4 colour hires by default, because hires is impressively businessy... but 8 or 16 colour hires would lock out the CPU most of the time, as the chipset would have to dip into the 68000's even cycle RAM accesses and stall it. 4 colour hires lets the CPU (on a chipmem-only system) run at full speed!
http://amigadev.elowar.com/read/ADCD_2.1/Hardware_Manual_gui...
Two big reasons. First, it's about running memory chips in parallel to increase bandwidth. Image data was hard to get to the screen fast enough with hardware in that era.
Second it allowed for simple backwards compatibility. Programs were used to writing directly to video memory, and in an EGA card the start of the video memory was valid CGA data. The rest of the colour data was in a separate bit plane.