Let me try and help you out here. A strikeout takes 4.8 pitches, a walk, 5.5. Everything else (mostly BIP) takes about 3.3. If you have a low BABIP, of course you’re going to be throwing fewer pitches because BIP take fewer pitches to throw.
1. BIP take fewer pitches to throw than K and BB. For this reason a pitcher having few BIP should have a lower P/PA than a pitcher with many BIP. But having a low BABIP is not the same as having few BIP, nor is a high BABIP the same as having many BIP. (K-rate does move things in that direction, but it’s a nudge, not a shove.) It does not necessarily follow from what you’re saying that low BABIP should produce lower P/PA (or vice-versa).
The only reason high-K rates don’t lead to higher pitch counts is because Ks are automatic outs and BIP aren’t, and the difference happens to cancel out. But that’s given an average BABIP. Obviously, if you have a low BABIP, it’s going to take you less pitches to get through a game, and vice-versa. So sorry, you haven’t solved anything.
2. He’s talking about pitches per plate appearance, not per game.
3. I think what dzop is saying is that low BABIP correlates with high P/PA, not low P/PA. That would mean his findings run counter to your explanation. (You say low BABIP should mean fewer pitches; he says low BABIP correlates with high P/PA.)
Having said all that…
4. He still hasn’t solved anything, unless (a) P/PA is predictive - IOW, this year’s P/PA for Pitcher X is predictive of next year’s P/PA for Pitcher X - and (b) the correlation between BABIP and P/PA holds up year to year. If both are true, then the unexplained, seemingly random variance in BABIP from year to year can be predicted. But given that year-to-year BABIP is not well-correlated, I can’t imagine that you can have both (a) and (b). If you have (a), that means year-to-year P/PA is correlated… but y-t-y BABIP isn’t, so the correlation between the two should be unstable. If you have (b), all you’ve done is to find that P/PA is a good proxy for BABIP… but if so, then (a) can’t be true.
If you can’t predict or project BABIP with it, P/PA is useless in this context other than to save a lot of spreadsheet work to get BABIP. That’s still quite useful, mind you. But it doesn’t “solve DIPS”.