I don't think there's an overarching rule that needs to be applied. In this particular example, I know Koestrizer competes in strongman, and there are plenty of events where knee wraps are allowed. And there are rarely straight up squatting events at lower level strongman shows. So if he is seeing the desired training effect from using the wraps, he's getting stronger, able to train frequently and with confidence, etc, then the wraps are probably a good idea.
I've seen guys with enormous, strong legs who train in wraps a lot, and I've seen guys with enormous, strong legs who never use wraps. Some guys who compete in wraps only start wearing them a few weeks out of competition, some train with them year-round. At the end of the day, I believe competent lifters are not putting their knees in harms way when they squat with wraps, so it really comes down to 'what do you want to do?'
I will disagree to an extent about 'it's not you lifting the weights it's the wraps'. I've heard the same thing said about a belt as well. It's simply not true. There are certainly muscles within the chain that have to work harder to squat 700 lbs wrapped than, say, 600 unwrapped. There is a benefit to the additional load for muscular development in my opinion. Belts don't lift weights, wraps don't lift weights. They are tools that, when used properly, allow you to move heavier loads.
If wraps were truly 'lifting the extra weight', there would be no reason for a lifter who competes wrapped to ever practice in them, right? As soon as they throw the wraps on, they should automatically add on the lbs, if that was the case.