No it is not subjective: Correct white balance means that a white, gray, black or full gray scale surface is displayed without discoloration and have the same RGB values from the whitest down to black .
One should distinguish between the use of gray cards that are more suited for exposure and not white balance and a card where the white balance should be made towards whiter area with a value around R 220 G 220 B220, . The cards should also have such metamerism characteristics that a white balance can be made in different color temperatures.
Best results do we get from a card with for example four different surfaces from black to white so that we can adjust curves towards more points than one grey.
And if the WB results not fit the taste - that is a subjective opinion and we can adjust cooler,warmer etc .
I use ColorChecker also for camera calibration in place and it still doesn't matter, because until you don't work in studio or with fully controlled light you get anyway the correct WB just in a place where you check it at specific angle and not for the whole scene. Since I have found out that, my workflow is much simpler because i simply don't use it everywhere nor always
Seriously - if you control the light, it helps a lot. If you don't have too much influence on that, then in most cases it's just a matter of taste.
Theoretically - you are right. In practice if you are a pro then go outside, measure the current temperature of the natural light, set your external lights to the same temperature, cast your light form ideal white or silver surfaces and then it makes sense. If your target has an ideal objective white balance with proper skin tones but the rest is ugly, then what a sense makes setting the WB to the correct WB just in this place?
What is the correct objective white balance in a scene with light sources having different temperature? What is the correct objective WB on the soccer field in the late afternoon when the external lights are on and have of course a different temperature than the sun at the sunset? You have three players in a frame and each of them is differently lit? I'd like to know it myself because neither of: set K, grey card, colorchecker (light changes through 90 minutes), auto, daylight or shadow help. And of course obtaining WB from white shirts of the players doesn't help, because it changes drammatically depending on the angle of the shirt exposed to either light, distance to the light and amount of the shadow on the shirt giving in the end different tones of the green, but correct tones of the skin etc.