My instincts about Maddux's BABIP were wrong. You're right, Maddux did beat the league average BABIP, particularly between 1992-1998 (see plot below). But you appear to be misunderstanding what I'm saying. I'm not saying Greg Maddux was just a "lucky" pitcher. He was an excellent pitcher. I'm saying that people conflate his remarkable ability to control the ball with him having the ability to also control where the ball goes after someone puts it into play. The extent to which pitchers actually have this ability is miniscule at best. It's probably at least an order of magnitude less than people are thinking of when they make that claim. Maddux rarely walked hitters. He led the league in BB/9 9 times, and was probably in the top 3 15 times or more. This was his superpower. As I mentioned earlier, there is some research (which I'd have to read again, it's been a while) that suggests a really strong pitcher may have a small, but measurable effect on their BABIP, but that estimate is only something like 5 points worth of BABIP, which is to say out of every 1,000 times a ball gets put into play, an elite pitcher is able to prevent an additional 5 of those into becoming hits than his peers (hence I said it's a tough sell). However, a pitcher's BABIP can often fluctuate 70 or 80 points from one season to the next. Even if 5 of those points are within their control, that still leaves 65 to 75 points worth of variance or "luck" which is completely outside of their control.
BABIP is a very useful statistic for putting other stats into context. It is influenced primarily by luck, but also by the defensive talent of the players on the field, the skill of the batters, and by the ballpark. Hitters have a fair amount of control over their BABIP numbers (though they are also very much subject to luck in the short term) as exit velocity is highly correlated to BABIP values. The harder you hit the ball, the more likely it is to drop in for a hit. But pitchers face an approximately uniform (top of the order inflated) distribution of batters, so hitting talent mostly evens out for them with some minor exceptions (e.g., pitching in the NL yields a slightly lower BABIP than the AL because of the DH spot, and pitching in a division that is stacked with good hitters can deflate your BABIP if you have a higher than average number of starts against strong offensive teams than your peers. But these effects are fairly small. The overwhelming majority of the variance in BABIP values is simply due to random chance. And this variance is actually pretty wide from season to season, and it correlates highly with the fluctuations you see with other stats that are highly subject to luck as well (like ERA and WHIP).
A pitcher like Maddux had a few things going for him which should have helped him outperform the league average BABIP numbers. He pitched in the NL, was in a pitcher's park, and had Andruw Jones chasing down balls for him in CF. I'm not sure exactly how much each of those factors weighs in exactly off the top of my head, but they do have a measurable impact. But even if it is true that a pitcher as great as Maddux is capable of "beating" the BABIP line, the evidence shows that it would only be to the tune of a few balls out of 1,000. That's certainly not what people who promote the idea that he can control ball flights with his pitching style mean when they make such claims. If playing in a pitcher's park is worth 1 or 2 balls per 1,000, and having Andruw Jones running down fly balls is worth 1 or 2 per 1,000, and pitching in the NL is worth 2-3 balls per 1,000 and having god-like control is worth 3-5 balls per 1,000, that would add up to someone like Maddux beating the BABIP line by 9 points.
If you haven't read it before, this is worth a read. It has a pretty good explanation of BABIP and why it's important.
https://library.fangraphs.com/pitching/babip/
And since I was wrong and am happy to admit when I'm wrong, here's a plot of Maddux vs the league average BABIP showing that he did in fact beat the league for a good several-year run in the 90s (note the blue line is MLB average, not NL average, which would be slightly lower).