Built around the Motorola MC6845 display controller, the CGA card featured several graphics and text modes. The highest resolution of any mode was 640×200, and the highest color depth supported was 4-bit (16 colors). [wikipedia.org]
That's technically true, but for all practical purposes, you got four colors and liked them. From your Wikipedia link, the 16 color mode was a special trick from 80x25 text mode. I played a lot of games on a CGA monitor--to this day, those godawful palettes are burned into my memory--and I don't recall ever seeing any game use that mode.
As for the PC speaker, I can remember the Windows driver that made it a PCM device, and it was passable but low-quality and used a lot of CPU. Some games made a valiant go of it, but there's a reason why the Adlib and Sound Blaster cards became so prevalent.