First let me start off by saying that Kalle Beck is a very well known strongman competitor among the community and that you'd be hard-pressed to find somebody out there who doesn't think that he is a beast, myself included. That being said, I found myself disagreeing with a recent video of his that he released in regards to programming squats for a strongman training routine.
Squat, bench and deadlift should always be your foundation for strongman. Squat to me is the most important exercise for strongman. Back squat in particular. Everyone believes front squats have more carry over into strongman but we are not Olympic lifters. We very rarely see a strongman competitor drop so far under the bar that it is necessary for front squat to be trained. Almost always, strongman competitors are just muscling the bar up to their chests or continental cleaning, which is a technique in strongman where you pull the bar up to your diaphragm and then bump it up into press position. With cleans like this, front squats are rendered obsolete.
In the video, Kalle Beck talks about how it is rare that there are not many squat specific events in strongman. In my opinion, I believe that almost every event depends on your ability to back squat, and yes, your single leg work such as lunges. Let's take a look at Circus Dumbbell, one of the many staples in strongman. After loading it onto your back, you're using a traditional squat to push the weight up and catch it at the top. Just watch multiple time World's Strongest Man Brian Shaw rep out the circus dumbbell like a pro.
As for press, whether the implement is axle or log, your leg drive is everything. Nothing builds more leg drive or force development than back squat. As for maxing out and rep ranges for squat in strongman, I believe they both are important to train. Nothing is better than maxing out on a lift and I do not believe that it is a waste of time. It's a great way to see how much stronger your legs have become and it's big in building mental toughness for the athletes. That said, training for reps is important as well. In strongman we usually have to rep out weights for a certain amount of time, so training muscular endurance is also key. To help max out and build my muscular endurance on squat I love programming in banded work. For strength you can never really go wrong with a banded squat using a 5X5 or a 3X3 program. On the flip side, using them for muscular endurance at high rep ranges such as 3X15 is a great way to help you push through that fatigue you get during competition. For moving implements such as yoke and farmers handles I agree that nothing will help you faster than single leg work. Producing the same amount of force from each leg is extremely important. This will point out any imbalances in your leg drive for your press as well. Think about holding 300 lbs and being ready to press but finding that you're unable to produce the same amount of force from each leg. Things like this can mean the difference between hitting or missing a lift.
Kalle Beck also talks about how front squat is important for stones and log clean and press. I believe stones and log training go hand in hand as well as any rounded implement such as keg clean and press. The movements are all the same. You pick the implement off the ground, lap it, and then get it to your chest like any other press implement. The only difference is that stones don't go over your head. Instead you push them onto a platform or over a bar directly in front of you.
As you can see in the video, yes, he does look like he is front squatting, but look how he leans back towards the top of the lift and his back produces somewhat of an arch. When you front squat this should not happen. As for coming out of the hole with stones, log cleans will help this far more than a front squat.
Notice how he leans backwards almost to get the weight up to the proper spot. Front squats will not help too much, especially technique wise. Instead of training front squat, I would train all forms of a deadlift. Conventional deadlift will be huge for your atlas stone lift. After all, if you cannot deadlift 300 lbs, you will not lap a 300 lb stone. An 18 inch deadlift will have significant carry over to your log clean and press. Using the same logic, if you can't pull 300 lbs to your hips, you won't pull the log into the correct cleaning position. My advice for improving your cleans on both of those implements is to practice them. Start with light weight and rack them into position as if you were going to load a stone or press a log. Just as you would program squats for max strength and for reps, I would do the same for deadlifts and cleans. That way you're fully prepared if you participate in a competition that requires an even such as "300 lb stone for reps." You can look at it confidently and think to yourself, "My max deadlift is much higher than that so lapping it will not be an issue. Plus my clean on stone is 320 lbs. Now I just have to practice a 300 lbs stone for as many reps as possible for whatever the time limit may be." That in my opinion will go much further than training front squat.
Powerlifting and strongman are different sports and I understand his point in that. Strongman does take more than brute strength. There is a lot of athleticism involved, and yes, it is true that someone might out deadlift you or out squat you but that does not mean they can finish a medley or carry farmers handles or a yoke faster than you. But some of strongman's best competitors have competed in powerlifting before entering the world of strongman. See strongman competitors such as the legendary Bill Kazmaier, who has won 3 World's Strongest Man titles, or the great Jón Páll Sigmarsson, aka "The Viking," who went on to win 4 World's Strongest Man titles, both of whom have competed in powerlifting.
In the end, being a great strongman competitor comes down the three things...
1. Know the implements
2. Train hard
3. Keep squatting