Receiving an allowance and having spending money is a foreign idea to most Amish children.
Neither LV or I received an allowance, and it's one of the things we carried over from being Amish, for the same reasons we didn't, our children also don't have money to spend.
Reasoning behind this is, a child should not have to worry about supplying their own needs. If they start saving and spending money for wants that will carry over into adulthood and cause them a lot of unnecessary financial burdens.
There is a big difference between wants and needs. Learning to be happy with what you have will be beneficial for the rest of their life. Buying things simply because you want them can be a hard habit to break.
It wasn't that we didn't have any money as a child, and our children also get to keep any money they earn, but they don't get to spend any of it until they have needs. The day they buy their own car or house, I know they will be glad for everything they saved, and hopefully they will still be happy to live their life knowing it isn't material things that bring happiness and satisfaction to their lives.