I started at 7, but I think that was a little early for me, I had trouble not blaming myself if we didn't win.
Since competitions are businesses, it's pointless to rely on them to set a cut off age, they just want your money. It's up to the studio to set a minimum age for competing. As a dance teacher, I've found that usually by age 10 the kids are aware enough to understand what they're doing and why. We have suspended kids from competing because of their school grades though and that's something else studios should consider. Not all kids can balance competition life and academic life, that doesn't mean they're bad at either but they have to have the discipline to do both.
Solos and duets can be a kicker though, kids should definitely be older (14/15) before taking on a solo, it can be really hard to deal with rejection/failure of such a personal nature before that.