As long as you teach your children to manage their money, they will not lose control using that money. They will know that getting money is not easy and they must work to earn money. They will not waste money for something they don't need but they will split the money based on their needs.
Perhaps, saving will be the first thing you can teach to your children as many parents do to their children. They also teach their children that they need to earn more money to fill their needs. So parents need to tell them that money is something they can use to fill their need but they should save their money for their future.
As their parents, we will give the lesson so they will not make a mistake related to managing the money. We know that they can lose control so we teach them to manage themselves. Every parents want to give the best for them so they will prepare many things for their children.
You see, at that very tender age, most children don't understand the difference between wants and needs. They really don't know what they want, so they just want to lay their hands on everything that attracts them at any point without knowing that there is a price that must be paid for it, which is money, and getting that money isn't something to template on because you must work for it.
Like you said, it's good for parents to teach their children how to save.
In as much as a child needs to enjoy being a child, a parent must let the child know that he/she doesn't need a particular thing that he/she has already got. If parents can interpret the principles of wants and needs, then I think the child has learned more than 30% on how to manage finance.