A local parent of an eight-year-old followed my blog and site and loved what we did and wanted to sign his kid up for lessons. I repeatedly told him "no," because at that age they should simply play for the fun of it. To get better, take some reps, throw "long toss" (aka play catch), and keep the game fun. And put down the equipment for 4-5 months every year.
That kid is now 11 years old and his father strongarmed me into training his 11U team, to which I finally acquiesced. And at 11U I'm fine with working with them twice per week, and they are throwing harder, staying healthier, and are way ahead of their peers (mean velocity is in the low 60's, which I guess is good for that age group).
And none of them had regimented training programs before they were 10. Even now, we keep it fun and don't overdo it.
Testosterone is the name of the game and understanding that there is a wide variation between biological and chronological ages is vital.
It ain't where you start. It's where you finish.