You asked my thoughts, ye been warned.
First, I think "high level S&C" is too vague in order to talk about whether or not kettlebells are useful for it or not. I immediately interpreted "high level" meaning "professional athlete" or at least "national-caliber competitive athlete." But sport makes a big difference doesn't it? I would say the juice wasn't worth the squeeze to make kettlebells the mainstay of a pro or college football S&C team, but I don't know if I'd say the same for, say, cross country runners.
If we lower the level to, say, high school athletics, while I think kettlebells could provide a sufficient stimulus I would be more concerned about setting up team sport athletes for success in a college program (or getting recruited to a college program). Teaching a high school football player how to properly squat, clean, bench etc. with a barbell is going to set them up better for success than teaching them kettlebells. If they going to move up to a "higher" program that will likely use barbells as the primary training implement then it is part of our job to prepare them for that - and that might be best done by training them with barbells, not kettlebells. (I realize that you said "high level S&C" so maybe this isn't a consideration, but since I've only worked with high school athletes, it is for me.)
Second, we have to establish how strong does an athlete need to be before strength is no longer the limiting factor. Then, we could assess whether that strength was best attained with a barbell or a kettlebell. I know a shot put coach that says that 400lbs bench and a 450lb squat are what you need to throw far (beyond that strength isn't the issue). Are kettlebells going to get them there? Probably not.
Third, we have to identify the ease of teaching the movements. I can teach barbell movements much quicker than I can kettlebells, but that just might be because I'm more experienced with barbells and teaching them.
Breaking down their video, their initial point about the center of mass was completely lost on me. I didn't follow their argument. I also didn't follow their argument about kettlebells beating people up too much because of all the eccentric forces.
They talk that the main point of the strength side of things is progressing weight, used in exercises that go through a full ROM, and that that requires something more easily adjustable than a kettlebell. I understand the benefit of the barbell being loadability, but their argument for it isn't an argument against kettlebells, as one can manipulate volume (sets and reps) as well as density (rest intervals) to progress in strength with kettlebells. A better argument - and one that I firmly stand behind - would be that kettlebells are topped out at much lower poundages - even if super large sized kettlebells were readily available, they become increasingly awkward to deal with in the form of doubles. A 100kg front squat is really no big deal, but a 2x48kg is much more challenging. A 200kg front squat is fairly common, but try doing a double kettlebell front squat with two 100kg kettlebells!
But even in this situation, it is sport- and level-dependent. While an NFL team might not be best-served by using kettlebells for strength purposes, a high school football team might, or possibly even a high level runner, or possibly even a college soccer team. There are lots of sports I don't know well (most winter sports, most track and field sports, etc.), so it is hard for me to say whether kettlebells would be equally suited to barbells. I've worked with high school girls volleyball teams and I think switching to a kettlebell would be fantastic. But again, when working with high school athletes, I want to set them up for success if they go to college, and part of that is teaching them how to use barbells as more than likely the college will.
This could be an argument that gets lost in the weeds, but they are arguing against a particular way of kettlebelling. This is similar to arguing against a particular way of Crossfitting, or even a particular way of strength training. What they describe as kettlebelling - light weights, lots of reps, maybe using a variety of exercise that is challenging with light weight - isn't the entirety of kettlebelling.
They had some other points that I agree with (training with kettlebells one quickly starts to need quite a few, and the cost and size quickly equal that of a bar and plates) and some that I kind of agree with (kettlebells are great for rehab or unilateral exercises) and some I disagree with (what we've always done works why innovate), but fundamentally they say that a good S&C program has a strength component, an anaerobic component, and an aerobic component and there is no disagreement there.
