And with all the writing about how old "aiki" is, remember another word, also using the composite of "onyomi and kunyomi" - KIAI - which is always, and definitely has been always read that way, not "goki."
Prof. Goldsbury just pointed out to me that "ki" is also considered to be kunyomi in some dictionaries, as well as onyomi, which means that both "aiki" and "kiai" can actually be read as purely Japanese words. Thus solving the on/kun mixing problem, such as it existed.
Since there is no apparently no pre-Chinese-influence Japanese word that has the same meaning as "ki" that I'm aware of, my guess is that it was such an important word culturally that it was adopted as kunyomi. Or that the dictionary compilers were trying to convince people that the Japanese invented the word.