I think that is an interesting and complicated question. Something to ponder. Who would test? Is there a business somewhere in that thought? Would you pay for it? I am not sure I would pay for testing to say "your kid should try this and that sport". I have tried hard to get my kids exposed to different sports and let them figure out things. Between the city rec stuff and their school - they have had a taste of many sports. There is a point that it is just too much. Earlier this year after football practice, which he was missing swim practice for, he brought me a flyer for wrestling. He hasn't had any time with it but I had to shoot that down quickly because it was just too much. He wasn't overly interested so it wasn't a big deal... if he was, maybe I would figure out a way to have him try it out and then decide if there was something he wanted to drop to do it.
I think it would almost certainly have to be a private business catering to people with money. If you think about how much parents will spend on travel hockey, private gymnastics instructors, QB camps or how early they will get up day after day to get their kid to swim practice, then I can imagine there is almost no limit to what many parents are willing to spend or do. I think many parents also have the hope that all the time and effort spent will be rewarded with an athletic scholarship for college. Testing might be able to point them in the right sport to maximize their kid's abilities.
Then what tests would you do? And how many of those can translate to a zillion sports... being 'fast' translates to a whole bunch of different sports and being tall or athletic or fast doesn't always translate to the sport as well. How many sports would be very hard to test for?
I have no idea. That would be something that a team of data scientists and kinesiologists would have to determine. No way it would ever be a perfect prediction. You would need more than speed for sure. Things like body composition (not just weight but weight distribution), slow twitch vs fast twitch muscle analysis, hand eye coordination, foot speed, decision making speed and some kind of body imaging.
But just being good at something doesn't mean they will like it either. My daughter would have done very well in swim- better than she does at volleyball and basketball but she has no interest in doing it. I overheard a conversation two groups of parents were having about one of the kids having had tried a ton of other sports and it wasn't that he was bad at them or anything, he just didn't like them but then did swim and loves it. The other parents were talking about how their son had done swimming for a while and for a long time just didn't seem interested. They were like, "I will show you old video of him, it looks like he is just going for a nice leisurely swim." and now apparently their boys are two of the better kids on the other team.
I would say it should also include some kind of interest test to. What types of exercises and activities would also pique the interest of the child. Solo vs team? High contact vs low contact? Fast paced vs slow paced? Maybe even have a set-up where kids can try a myriad of sports- even ones that they might not typically think of like rowing or archery.
My daughter is another example. The only reason she did volleyball and basketball last year was because her friends were doing it. She liked volleyball and not so much basketball. Then over the summer, I had her in a bunch of volleyball camps, clinics, etc and some basketball too. She improved in basketball a lot and enjoyed it much more this year.
Then there is accessibility. Some sports cost more than others and some areas of the country are more focused on particular sports than others. We all know Texas is football crazy... I am not sure how big their hockey leagues are though (I could be wrong but I am pretty confident not nearly as big as their football leagues). I had my kids do a city rec archery class to get them exposed to it. They really enjoyed it and would easily have done more but the only decent place I could find isn't exactly a short drive... not too long but long enough to be a factor. Add in them being involved in other sports etc and I just didn't pursue it more for them. Archery would be a good sport to ask how do you test for it? Even if you have them actually try it, the first attempts are universally bad.
Yes accessibility is a major issue. Tough to find a rowing club Albuquerque. Again, I would imagine this is mostly for the well to do. Really it's probably more like a Soviet era project that they would force every kid into. Obviously, I don't support that use. Just something I've thought about for awhile that I am surprised doesn't exist (that I am aware of). It seems like there are always new industries coming up to make money off of youth sports. Seems like an avenue untapped.