TM: If you had to choose between the free squat and the box squat, what would you choose? My no BS, non-PC answer is this: free squats will trump anything in the weight room for sports. The recovery time is slower than box squats, but that should tell you something- it's a harder movement and requires more muscle, coordination, strength, etc.
This is easily seen by leg (quad and hamstring) and glute development of a free squatter vs. a box squatter. Box squatters usually have comparatively poor leg development. Some people will argue that you can make up for it with lunges, step-ups, or something similar. But all this tells me is that you could kill two birds with one stone simply by squatting without a box. (Remember training economy? You should, it's important).
Also, remember that teaching a free squat and having athletes do it correctly isn't as hard as you're probably making it. They DO NOT have to be 100% correct with their form; I'm not even close to what most people will say is perfect squat form, but I still get a lot out of it.
I believe that it's easier to teach box squats, but most of the problems that people have squatting (besides being scared or whatever) stems from lacking the proper mobility. To me, training for sports is two things: 1) Having the mobility to get into the proper position for sporting performance, and 2) Having the strength to maintain the position or move from the position.
That's really it. If someone can perform a free squat correctly, or at least fairly correct, that tells me that they're probably mobile enough to do most anything on the court, ice, or field. (Not always, mind you, but it's a good indicator.) So perhaps those guys who absolutely suck at free squats need their training to address the other problems that they're having.
I also think that three to four workouts to "find" their squat form is fine. You can use these weeks for some lower volume/less intensity work and have them build from there.
But I'm not entirely convinced that one needs to throw away the box squat either as it does have great applications, especially for those with knee problems. And some people are just awful free squatters...AWFUL. For these people, the box is fine.
Just remember that you have to treat the box squat as a separate exercise. Many lifters make the mistake of getting good at box squats, thinking that there is a carryover to free squats; it's only when they go out to free squat and shit themselves miserably that they realize that the carryover is limited at best.
That brings me to something that I've learned the hard way- the box squat transfers better to a geared free squat than to a raw free squat. I've seen this in my own training and countless others. Remember, a squat suit will stop you in the hole, much like a box would. And the suit/briefs will rocket you out of the hole, too.
So getting back to whether to choose a free squat or a box squat, the real question you have to ask is this: is it important to be good at the free squat, or is it just important that you (or your athletes) perform a squatting movement of some type i.e. box, free, Zercher, belt, etc?
You have to determine that for yourself, but in a perfect world, the free squat would be the number one squatting exercise for me.