The question: how do developers of cameras, raw converters, etc. pick the min and max value for white balance slider? Is there any science behind it?
The color temperature in white balance selector is based on physics, the so-called black-body radiation. Black body radiation gives the spectrum of electromagnetic radiation (in this case, visible light) that a black body at a given temperature emits to its surroundings. That's why it uses a unit of temperature, Kelvin. Imagine a piece of iron being heated on fire: First it is black, then deep red, then orange, and yellow, and so forth.
Using the theoretical spectrum, we can therefore map a temperature, say, 2000 K, to a color. From a physical perspective, the lower and upper bounds to the color temperature are about 1000 and 20000 K, marking the bounds of visible light.
In photo editing software, choosing the white balance only means that we want to choose the reference point against which all colors are defined. The color temperature is a good starting point, as most light sources are in fact (approximately) black bodies that radiate light (for example, tungsten bulbs and the sun).
As others have pointed out, the temperature only defines one axis in the two-dimensional color space, ranging from red to blue colors. In addition, most editing software have another variable that is perpendicular (that is, independent) of the color temperature to tweak the white balance further. This axis is often called tint, mapping from purple to green colors. Note that while the color temperature is well-defined, the tint variable is not, and it can differ greatly between software.
All cameras have been calibrated to reproduce realistic colors, that is, to reproduce colors as the human eye sees them. This is based on extensive measurements of the human color vision. Empirical color spaces, such as CIE 1931 RGB and CIE 1931 XYZ color spaces, map all possible colors that are visible to the human eye. Cameras have been calibrated to reproduce colors in these color spaces as accurately as possible, given the limitations of the technology (no camera, nor a display, can reproduce all visible colors).
This means that if you set the white balance in your camera to 5780 K, you should get realistic colors as they appear in direct sunlight. The same is true for your post-processing software. However, you never know how well the manufacturer has calibrated the camera/software. In my experience, especially photo editing software can be somewhat loose in their definition of the white balance. Camera manufacturers may limit their color temperature range to what they believe their products can reasonably reproduce.