Early home computers and game consoles output video to TV sets. The NTSC color clock frequency is 3.58 MHz. This informed the design of some video systems: http://pineight.com/mw/index.php?title=Dot_clock_rates
In particular, the Atari 2600 and Intellivision have one pixel per color clock, which is an obviously reasonable way to do it.
In the Apple II, the pixel clock is exactly twice the color clock. That makes sense because it has an option to turn off the color clock to generate reasonably crisp black-and-white text, then turn it on for the ability to generate artifact colors. This arrangement is very economical on parts count, which was important at the time.
The Atari 800 also has a pixel clock exactly twice the color clock, but as far as I know, it does not have the option to turn off the color clock. I'm trying to figure out what advantage it gains from this.
Specifically, I know if you run at an exact multiple of the color clock you can generate artifact colors, but surely you would get strictly better results by running exactly at the color clock and spending the memory and bandwidth on coloring fewer pixels? For example, say the Atari is operating in a mode with 1 bit per pixel, and generating artifact colors. Would it not be better off halving the pixel resolution and using 2 bits per pixel to just generate the wider range of colors directly?
There is a theory that says it makes sense to subsample the chroma information, in other words run the luma information at twice the frequency, because the luma information is more important, but as far as I can see based on e.g. https://en.wikipedia.org/wiki/Apple_II_graphics#Color_on_the_Apple_II the result of this is that the luma information simply gets converted into artifact colors, and you might as well have done this directly.
The situation with other machines like the NES looks even worse; it outputs somewhat more than one pixel per color clock, but less than two, so that the extra resolution will just convert into uncontrollable color fringing. On the face of it, the NES looks like a reduction of the resolution to 3.58 MHz pixel clock would produce better results for lower cost.
What advantage was there in going higher than one pixel per color clock (in machines that weren't going to turn off the color clock to generate black-and-white text like the Apple II), that I am missing?