China and the US aren't just doing well because their pool of selection is so much bigger - that's a massive smoke screen. Jamaica is a tiny island and they are dominating athletics.
It's also because in the US and China they have a very competitive spirit - there is a lot of merit in being good at sports, they are encouraged, rewarded, supported, it is closely linked with school and education and sports are a route to success in a way that is just not supported in this country.
Jamaica, a much smaller, poorer country than us, have athletics as a way of life. Their athletes are supported, coached and shown in a highly respectful way - unlike us with our money-grabbing, abusive, misogynistic, rock-star lifestyle footballers 
We don't support or provide anywhere near that kind of infrastructure. Most of our athletes have second jobs and there's no link up between after school sports clubs and schools. We just don't support any athlete outside of football in the way other countries do. That is the main reason we're trailing behind in the medals tables - yeah we're third. but look by how much!
And yes, completely agree with Bonsoir about the distinction between competitive sports and movement. We should be doing everything we can to get children away from the TV and gaming consoles, and getting them outside moving more.
And yes yes to Rubyfakenails about the uneducated view of boxing/martial arts. I grew up with martial arts, DH works in an elite boxing gym - yes, some clubs are about pure aggression and are seedy. Yes it has resulted in brain injuries for some. But you've obviously never done it if you don't get the intense fitness, strength and discipline required. It's not just people bashing people's heads in. It's like Mixed Martial Arts - ubiquitously named cage fighting - those people are insanely fit and dedicate their lives to training different disciplines to master them all - I would kill to be that fit!
Nature versus nurture. There is an argument for why Jamaica dominate athletics - accelerated selection. DH is mixed race - his paternal family were almost certainly of slave lineage. He is INSANELY naturally fit, strong and talented at pretty much any sport he turns his hand at. I asked him last night how much he thought his genes contributed to that - he shrugged and said of course it had something to do with it but it was growing up seeing his parents getting out and doing stuff, always sporty, involved in club sports, that really impacted on him. We will never be a competitive country that values sports and the merits of movement and a competitive spirit while we're showing our children it's OK to mooch around on the couch.