The usefulness of things such as color checkers is precisely because all of these things are not usually known to the degree needed. Particularly, the final two on your list are often totally unknown at the time the image is taken.

In addition to your list, the exact nature of the lighting in the shooting environment is often not precisely known. This is perhaps the most important reason to use a color checker along with a gray card (which, incidentally, is primarily a tool for calibrating exposure, not color).

Just one example:

You can say outdoors under a sunny sky is a certain "color", say 5500K, but there is still a long list of variables that will affect the exact nature of that light and the results of photos taken under such a sky. These things can affect not only the color along the Blue←→Amber color temperature axis, but also the "tint" along the more or less perpendicular Green←→Magenta axis. A few are:

• The height of the sun on the sky. The closer to the horizon, the more atmosphere the sun's light passes through to reach where you are shooting.
• The atmospheric conditions of the parts of the earth's atmosphere that the sun's light passes through. The amount of water vapor, dust, and other particulates in the air can have a profound effect on what portions of the spectrum of the sun's total output reaches a specific location. This can be constantly changing.
• The amount, density, and angle to the sun of any clouds in the sky. This can be constantly changing.
• The color and reflectivity of the landscape. Sunlight is reflected off everything you see outside during the day. A green lawn will affect the color of light on your subjects differently than a sandy beach, or snow cover, or a field of yellow sunflowers, etc. Foliage and vegetation are highly variable from one type of plant to the next.

The same is true of many environments lit by artificial lighting. Even if the exact type of lighting is known there are still many variables:

• The output of a given type light may not be as consistent as we need. Many types of lighting can vary by significant amounts from one example to the next. The same bulb can vary with the exact amount of voltage flowing through it, will change as the bulb ages, etc.
• Environmental factors play a role here as well. Different floor, wall, and ceiling treatments will affect the color of things in a room.
• It gets even more complex in environments with mixed lighting. The proportion of influence that each source has on a subject will vary by the subjects position in the room, by the camera angle, etc.

In the end, knowing the camera's reaction to specific wavelengths and intensities of light is not enough unless we also know just as precisely the nature of the light falling upon and being reflected upon our subjects.