It wasn't about tanking the club, just tapping the brakes. Retaining the fundamentals of the club's value, while minimising the extent to which that value could ever be realised by other investors, especially Usmanov.
Fundamentals doesn't even mean being top four or being in Europe, it's been about being able to return to the top four with a predictable amount of investment, and about maintaining the perception of incumbency among the league's elite clubs.
In the end KSE bought Usmanov out with an offer that exceeded a pro rata 30% of the club's then cap by a fair amount, around £100m I would guess. And that was after the club fell out of the Champions League.
My guess: KSE made that decisive offer because they saw substantial investment was needed at that stage, so the club didn't fall away far enough their growth strategy was jeopardised. And they wanted to do it with Usmanov (and the ghost of Dein) wholly out of the picture.
The comforting thing about the last few years of KSE administration of the club is that I'm now certain they care about Arsenal's progress as an investment, and know what they're doing. Doesn't mean they have any testable commitment to winning trophies, but at least they're not morons.