I'm not even sure this is what I'd conclude from this thread, and I'm a kettlebell lover, but like I've pointed out I think above, the S&S programme gave me a _base_ of strength to get to a higher level of judo. Barbell deadlifts and presses (with kettlebells and the barbell) also pushed my strength up which had a positive effect on my judo performance. Once up to a kind of limit (S&S with 32kg for swings and 40kg for TGUs, and a 370lbs deadlift, 32kg kettlebell press for three reps per arm per set) I got so into training for judo and kendo that I had almost no energy left for weights, and I'd say this situation went on a good 8 months until Quarantine set in. Now I'm back at my weights like never before. It took me a week to get back to where I left off at weights. This has something to do with muscle memory of course but I'm sure the judo and kendo kept me pretty strong too.
Kenny Croxdale knows what he is talking about and he is kind enough to post here for us. Evidently any kind of big pull movement is going to help with wrestling and judo and likely BJJ too, so cleans, swings, the deadlift, but if we're after maximum strength, I'm pretty sure the deadlift wins, and we are after maximum strength - power comes from adding speed to the strength, and the speed tends to be movement specific - so a product of on the mat training and experience over some kind of off-mat speed training.