This only tends to be in HID or Fluorescent lighting and now LED
But anyway considering when you go to a hardware store to look at the fluorescent light or HID section you see lots of CW, yes I'm aware that there is some variety of colors' but most is CW or CWX

Secondly why is CW called "Cool White" despite of it's soft(ish) appearance

I've actually been kinda wondering that myself all these years..

It's a nice neutral color.  Not as annoying and hard on the eyes as daylight, and not too warm or muted and gets drowned out like warm white does.  Warm white is a great color for environments that have warm colors on the wall, ceiling, and floor- or where you want to have a relaxed environment-  (churches, hospital rooms, bathrooms, kitchens)

The required color depends on the intended mood, but as well on the illumination level.
For low levels, typical at homes, you need to be around 2500..4500K, higher CCT would look harsh bluish.

For high illumination levels like work lights and so on you need colder light, about in the 4000..6500K range, warmer light would look harsh yellow.

And the "CW" (aka ~4000K) is just usable for both, not really optimal, but still fits. Hence sometimes called "universal white" (mainly in the German territory). And that means unless there is any technical obstacle (e.g. with HPS), the CW is the first color to be designed with any light source...

But then CFLs and general use LEDs are soft white for the most part

But then CFLs and general use LEDs are soft white for the most part

Because these are intended for the lower intensity home use, where the expected illumination level is in the area where these colors are fine. The thing is, for an eventual higher intensity use, where the colder temperature would be required, these CFLs and LEDs have too low light output, so the installation would have to use impractically high number of them to reach the higher levels.
Don't forget the rather typical F32T8 fluorescent emits nearly 3000lm, with most common two lamp per fixture it means 6000lm, while typical installation (e.g. over a single shop work bench) is two such fixtures. Having the same from incandescents (or equivalents) means 8x"100W", that is just too complex (once the fluorescents became available).
Normal application for the CFLs or similar is 1x or 2x per room way bigger than that work bench, so way less than 1/4 lighting levels. That is quite significant difference...

Plus unlike the workbench, at homes you usually want more relaxing atmosphere and for that the 4000K is still quite high.

They do make CFLs with a 4100K temp. I have a few.

They do make CFLs with a 4100K temp. I have a few.

They do, even the colder tones. The same as they do make the standard fluorescents, as well as HIDs in the warm colors.
But the point was, the mainstream is the soft white with CFLs/"incandescent retrofit" LEDs, but cool white with normal fluorescents and (high color quality quality) HIDs.

Most retailers now use SP35s or SP41s. They have a brighter, warmer color than CW,CWX, or even WW. Even though SP41s have the same color temp(4100k) as CW, they are slightly warmer and brighter.

然而我们的大部分都是DAY LIGHT，代码是“D”，以中国的电光源命名系统代码是“RR”，COOL WHITE的是“RL”

表示灯的色温的符号
RR：表示日光色（色温6500K）
RZ：表示中性白色（色温5000K）
RL：表示冷白色（色温4000K）
RB：表示白色（色温3500K）
RN：表示暖白色（色温3000K）
RD：表示白炽灯色（色温2700K）

Unfortunately I don't understand ehy CW is so common. To be honest, I don't like it at all, the halophosphor CW (640). In my opinion, it belongs at maximum to a parking lot or a barely visited storage room. It looks just grey and ugly.

Point of interest:
Here in Switzerland, we used to fit fluorescent fixtures very often with Philips color 33 and Osram color 20 (640 standard CW). Here were around 50% of all installed tubes these 640's.
In Germany, they had installed the same amount of tubes in color 25 (740, Universal white), which js a bit less efficient than CW, but much better color.