Info
HSpilot23
The ADC merely has inputs from pitot and static sources and Total Air temperature.
The corrections that you want depend on such things as your height above the altimeter setting source. As you can read in the first line, that is something unknown to the ADC.
Remember that Air Data are there, not only to keep you free from contact with the ground, but also to keep you separate from the other guys flying around - and for that last task, every Air Data unit has to work according to the principle numbers one, STANDARD, atmosphere.
The flip side of that airborne separation requirement is that you have to make corrections for ground separation related altitudes in vastly non-standard conditions.
(edit for a typo)