I don't think it should be surprising at all that hits are the strongest predictor of scoring. After all, hits are the primary way of getting on base as well as the only way to hit for power. I don't think any sabermetrician would doubt that hits correlate strongest with runs scored. Instead, I think sabermetrics would predict that just as OBP and SLG correlate strongest with hitter's scoring (as you said in your introduction), OBP-against and SLG-against would correlate strongest with a pitcher allowing runs to score. The correlations you ran of H/9, BB/9, HR/9 and SO/9 are basically serving as proxies for OBP-against and SLG-against when compared to ERA. And just as we might expect, H/9 is the best proxy for both OBP- and SLG-against because, again, hits are the most common way to get on base and the only way to slug. Of course, HR/9 was also highly correlated with scoring because of its major relationship to slugging (and it's minor relationship to getting on base). Predictably, BB/9 and SO/9 did not correlate as well with runs allowed because of their more tangential relationship to OBP. So all in all, your study basically showed (through proxies of varying quality) that whereas OBP and SLG are the best tools around which to build an offense, their prevention is the best way to guarantee a low ERA. Just for fun, I downloaded your table and made a down-and-dirty version of OBP-against by taking H, BB, IBB, and HBP over batters faced. The correlation between H/9 and R/G per your table was .882. The correlation for OBP-against? .886. Similarly, I made a REALLY down-and-dirty estimation of SLG-against. I tried to estimate total bases by taking all hits and adding the three extra bases for each home run allowed. Then I divided this by batters faced minus BBs, IBBs, and HBPs. While this "semi-slugging" percentage was much lower than the actual slugging percentages, I figured the differences among teams would hold up alright. The result? A .869 correlation, much higher than HR/9 alone. Now your last question was your best: What prevents hits (or more accurately, OBP and SLG)? Here is where K rate becomes important. But all sabermetricians would agree that BB rate and GB rate are important too. The problem with a "pitch to contact" philosophy is its reliance on the shakier idea that pitchers can control their BABIP and the hitting profile of the batters they face (ie their power). But if you're willing to concede that pitch-to-contact-if-you-induce-groundballs is a philosophy, then I'm sure many sabermetricians would take that just as often as high strikeout rates.
