Purely guessing, from the seat of my pants.
One of the things that a formula like DIPS ERA is doing (because it was developed as a predictive tool rather than a method to analyze performance) is predicting BABIP or $H or whatever you wish to call it. What such a figure “should be”. This is implicit in that DIPS ERA does.
The reason why (in my view) H or BABIP or $H or what have you isn’t needed in the DERA formula, and why it doesn’t improve the predictive power of it when it’s included, is that K rate (supplemented suitably by HR rate and a bit by walk rate) is a better predictor of future BABIP or $H, than BABIP or $H itself. Guys who are difficult to hit are, shockingly enough, difficult to hit. (This is the point that 90% of the research on hit rates and BABIP has ignored… yes pitchers differ in their abilities to lower BABIP; it’s just that those pitchers are roughly ordered by K rate, suitably expressed).
But what K rate to use? K/IP, which is roughly measuring K/AO, is likely a better overall predictor of BABIP than K/PA, because it hauls the outliers in. Guys who are very BABIP-lucky (from good luck or good defense) will have a better relative K/PA than K/AO. Guys who are very BABIP-unlucky (from bad luck or bad defense) will have a better K/AO (relatively) than K/PA. So K/AO will probably work better as a measure of strikeout ability as it relates to its prediction of $H or BABIP.
This is what I believe - it may not be true, but it is the explanation that best fits (in my view) with all the research I’ve seen on this topic.