I think, and I could be wrong, that they only accept driving because driving has your championship class (aka: Stakes).
According to AMHR Rulebook:
Method: All-Star points divided by number of shows shown at times, number of different judges divided by number of shows shown at times, number of horses/ponies beat divided by number of shows shown at times, number of Grand Champions divided by number of shows shown at.
So if thats the case they would only consider the driving portion because they are the only performance classes that has championship classes.
I thought they would include everything performance wise for your performance horse of the year, but guess not. Not according to the rulebook anyways.