Here is a take from a military guy.
Strongman training in the purest sense is horrible for the military because the tests the military does to qualify "fitness" have absolutely nothing to do with Strongman type competitions. Honestly - the military doesn't care how much you squat or deadlift. If they did, their globo-style gyms would be set up this way. They are not throughout the vast majority of them. They involve a ton of treadmills, and iron weights that cannot be dropped. For about 1/100th the price (and I've done the math) you could outfit a gym at any base that would be better suited for the military's needs. It isn't happening anytime soon though, so thanks for your wasted tax dollars.
Would it be great training overall? Sure. But GPP programs (i.e. CrossFit) work better to pass the test, and keep your level of work high for longer periods of time.
You put a bunch of fat/lazy Air Force people through strongman training, they still won't pass the run, and I would say as an AF member that 90%+ failures of the PFT are due to slow run times (and we are talking you need to run 1.5 miles in 13 minutes here people). This is of course often related to a crappy diet.
Please don't get me wrong, I think Strongman training is awesome. But it isn't the answer to the military's problem. Fit people in the military stay fit regardless, and the majority who pass with 100s can run well and have a slim waistline. The overwhelming majority though have more issues that need to be reconciled first.
Edit: Reread the first post - the sprinting/endurance work is the key, not the Strongman part. You could do SS or the CA WODS (which I do) and pass the test with 100% and be strong as a bull.