It’s an interesting question and one I’m not sure I can answer to the level I’d like to be able to. Here’s what we know, Belichick always seems to really keep thing simple schematically early on, at least on defense. As the season progresses we see more and more wrinkles, different personnel groupings, more exotic blitzes, etc.
My educated guess relates to BB being, in essence, a coach who believes in execution over scheming to produce results. It’s about sound defense, with everyone on the same page, and each “doing their job” and focusing on winning their matchups.
So it’s about simplicity but also with disguise. You hear a lot about how the Pats’ defense is a full of adjustments for every shift and motion the offense does. That was a weakness Mangini tried to expose when he was coaching, specifically with the Browns. When the Pats defense was young and inexperienced in 2009/2010, it was easy to throw a bunch of shifts and them, then expose their mis-adjustments.
So this is why I put a lot of stock into having continuity on defense. There is so much communication that goes on for them, the more experience they have doing that, the better and quicker they can be, and you’ll notice now that everyone quickly adjusts when Mayo calls out checks.