CRTs additionally impose their own limit on how sharp the picture can get horizontally. Confusingly, these are called "television lines", even though you'd think that refers to the horizontal scanlines that do discretely divide up the picture vertically. Color CRTs further limit the amount of color resolution independent of luminance resolution, and how they do that depends on what specific phosphor pattern they use, how they separate electrons from each color gun, etc.
[0] And one that's just as misleading as sample-and-hold diagrams of digital audio that make people go out and buy really expensive DACs for reproducing ultrasonics they can't hear
The colour was created by different phosphors on the inside of the screen, there was nothing different about the electron beams. The number and pitch, the resolution, of these different phosphor dots determined the resolution of the screen.
The shadow masking was to prevent the beam for, say, the red phosphors sweeping blue/green subpixels when moving from one pixel to another, since it wasn't practical to turn the beam off and then back on once the steering coils had been changed. Steering was continuous, so without shadowmasks, you would illuminate on the neighbour subpixels you pass on the way.
You could have done it all with a single beam, if you really wanted, but it's not very practical - you'd need to sweep slower since you could only illuminate 1 subpixel at a time, it'd take much longer to to steer, illuminate at the right level, and move to the next with the right beam power selected.
I think he described exactly what you did (in fewer words) in the second half of his post. ("Your typical color TV ..."
The first half discusses that some projection screens had 3 different tubes. ("Very few broadcast TVs ...")
Either that or he edited his post.
Let's say you're displaying a 640x480 screen on a TV. Your chroma information is sampled from an area about 2.1 pixels wide. So even if the signal is continuous, your color information is the result of sampling a boxed area centered on that pixel.
And because you don't want the wave pattern to be displayed as luma, you also take the average luma of that area. Now you have a blurred fat color pixel, but it can be positioned anywhere continuously.
Furthermore, even when using NTSC video timings, the 3.58 MHz subcarrier is specific to transmission of composite video (carrying brightness and color combined in the same signal). A DVD player for instance with a component or SVideo output produces NTSC timing but there is no subcarrier because the color signal is discrete.
To the number of horizontal pixels is essentially limitless (if you ignore the bandwidth limit and the CRT scan raster) while the number of vertical pixels/lines is always discrete.
