I feel like my point is being missed about single leg training. I don't mean that single leg training mimics PK training in a specific way. It's just a different way of getting GPP. Balancing on a slackline and balancing on one foot for a bulgarain split squat are not the same - the slackline is unstable and requires almost completely technical skill, whereas the split squat only requires base level balance on a stable surface than all strength after that.
The point I'm trying to make about single leg training is that you can build up as much if not close to as much strength using those methods as you can bilateral exercises, and with less chance of injury and burnout because of the reduced weight. If you have balance issues on one leg you shouldn't be doing heavy squats or deadlifts anyway, IMO, because your other leg will be working harder to compensate.
Why do you say a bulgarian split squat is a poor way to build strength? Because it uses less weight? But truth is after learning the exercise you can load up more than half of the weight you could handle on two legs onto a single leg. Strength coach Ben Bruno explains.
"While the overall loads will undoubtedly be less than in a traditional bilateral squat, the comparative load on each leg will generally be much higher. In my experience, after some practice getting used to the movement, most athletes will use 65-85% percent of the loads they use in the back squat, and this is on one leg. The number is typically closer to 75%, and in some cases, the numbers are virtually identical with athletes with back squatting technique. Personally, I have repped out upwards of 275 lbs on the RFESS and could not come close to squatting 550 for reps, or even 405 for that matter. Of course, some people will argue that the rear leg provides some assistance during the RFESS, and I will submit that it surely does. Nevertheless, the disparity is just too large to ignore. To understand this phenomenon further, you may want to look into something known as the bilateral deficit."http://www.dieselcrew.com/7-awesome-single-leg-squat-variations-and-why-you-should-be-doing-them
Single leg strength training is meant to be a comparative but safer way to strengthen the lower body, not as a poor substitute. I am not denying the effectiveness of squats and deadlifts. I am questioning the mentality that they MUST be done to see results. A rock and a hammer will both get the job done of slamming in a nail, but the hammer is a more focused tool that won't potentially damage the surrounding wood in the process. That is how I look at bilateral vs. unilateral training.
Box jumping a massive height will come from great strength. I submit that great strength can be built with a mixture of methods, not just one.
Squats and deadlifts are proven to work. If they work for you and don't beat you up too much go for it. If they don't, because of mobility, past injuries, CNS fatigue, or simply a dislike, why force yourself to? Coaches have proven other methods to work and science is beginning to back that up.
To finish, I also submit this interesting article. How Much Strength Do Athletes Need?
Parkour is a highly explosive and strength based practice, but ultimately, you have to decide how much strength you really need and where that strength will come from. For my money, I like to use as many bulagrain split squats, skater squats, and single leg hip thrusts
as I do deadlifts and back squats.