I'm a Capoeira teacher (at Ido Portal's place, Hacasa). I started coaching the youngest kids there (ages 3-9) two years ago.
The kids call it "Capoeira" but my goal is pretty much what you described up there: to give them a broad base of athleticism, coordination, and confidence without specializing in anything, until they are old enough to choose their sport. I feel gymnastics gives a good base and it is always mixed with basic ball games, baby-Capoeira (as much partner interaction for as little technique as possible), percussion, "parkour" leaps, circus stuff... Occasionally I take them out to the park to walk on the slack line.
I have a 5-year-old who has been coming to my classes since I got started. A little while ago he was bouncing on a springy mattress and called out, "Gittit, look at me, I'm doing a salto
(back tuck)!" and he did a back handspring. It was a little to one side but he had never learned to - he just decided to jump backwards onto his hands, and he did. He is years ahead of the others in some things. I'm awfully proud of this tyke and like to think I had something to do with this
That's it, I don't have anything scientific to contribute, I'm learning a lot now experimenting on the kids.