No, they wouldn't. For one thing, you've got to find something for them to do that involves actual "work and success."
How do you propose to provide that?
That depends on the circumstances, but opportunities exist in every family. Yes, begin with cleaning the table, buying groceries, paper routes, babysitting or cleaning a mechanic's shop, summer jobs at McDonald's, etc.
In 1980s, Oprah had as a guest Malcolm Forbes, a flamboyant "rich" man that lived up his wealth. She asked him an intelligent question, to wit: "With all this wealth, with all those boat parties, how do you raise your children with any sense of normality?"
He replied: "Boat parties? My children HATED boat parties. They were the ones cleaning the boat after the parties."
That alone answers your question.
In the previous post, I forgot to mention volunteering if everything else fails.
When my daughter was 12 she volunteered to babysit at a church during Christmas services. As you know, it's hard to find a babysitter for those days, since majority of people in this country are Christian and celebrate that holiday themselves. My daughter thought that she can fill the need because she is Jewish, and she would help our Cristian neighbors celebrate their holiday. So she babysat at a church (free of charge). I was really, really proud of her because she came up with this idea by herself.
So even one does not need the money (it was not the case in my family, believe me; I was in graduate school at the time), our children can always find work and take some responsibility.