As you mention yourself, different wavelengths behave differently through the atmosphere. In theory, this can be counteracted through atmospheric correction, however, modelling the atmosphere accurately is a complicated matter, especially for medium and high resolution satellites where the required information is not acquired along with the images (due to spectral constraints).
Performing an atmospheric correction requires modelling the path and interactions that the light will take through the atmosphere. When that path is long, as it is when either the sun and/or the sensor zenith angle is high, the light will be scattered more and the artifacts start appearing. To counteract this, a set of correction factors are calculated. Some satellites (usually coarse resolution satellites) carry sensors to acquire the information required to calculate these corrections factors.
However, when working with medium and high resolution imagery, you'll usually be looking at retrieving atmospheric parameters from coarse resolution imagery (usually only available in situations with "normal"/"low" solar zenith angles) or modeled data. This works well for low zenith angles, but when working with high zenith angles, the light will have passed through multiple "pixels" worth of atmospheric parameters required for determining the correction parameters - atmospheric parameters that usually aren't provided with enough variability as a function of elevation.
All in all, while the imagery can be corrected sufficiently with full information, getting that information without a significant field campaign coinciding with the imagery acquisition is not feasible. As such, it is more palatable to reduce the amount of trouble that you're facing, by limiting the solar zenith angle. Due to the sun-synchronous orbits of the majority of EO-satellites, the limit on solar zenith angle only means that acquisitions in the regions far from equator are rejected during the local winter, which in general is of little concern, due to the high snow cover in those areas that those times.