Here are a couple of articles about ages and stages of youth development that might be helpful.
I find the 9-11 year range pretty fascinating when it comes to bikes, as you can really begin to see some of the independence begin to form. You could probably look at some of the characteristics within the development stages and make an argument of how earn-a-bike would make a positive addition to these stages of development. You could also look at that 6-11 year old age groups and see how some of those ages might be a little young to go through the requirements of some earn-a-bike programs.
At the Boise Bicycle Project, we donate bikes to kids 11 and under and have an EAB program for kids 12-18 years old. In our experience, we've found a lot of kids lack the independence to get down to our workspace one their own, making Earn-a-bike a lot more difficult. We've also found the attentions span at that age makes it more difficult to have a more lengthy structured program. There are definitely exceptions, and we've allowed some younger kids in to our EAB programs.
For those kids under 12, our bike giveaway program still requires a completion of a 30 minute bike safety class that we hold at the same time they get their bike. You could argue that this is earning component, where the kids are still investing some time.
Hopefully those articles can help provide a little assistance. Good luck!