Hmm... I performed a quick test on iOS and, at least on my phone, autocorrect does not change "OK" to "Okay".
Appreciate you checking that. Didn't even cross my mind to do it on my phone right by me.
Your phone idea might be on the right track tho - for those of us who are so old that we used SMS before T9 was invented, typing 'kk' would be way quicker than 'ok'.
Just a thought.