I guess it is bad idea to hide any income or money saved or invested for "training" a offspring. Sure, being transparent might make them demand to purchase something, but then educating them about good and bad investments will be better. It will be bad to give them big money before they are mature, but they should at the least know the resources and funds stored or earned for them and for their future by their parents, because death is certain and can come at anytime and all those complications like "hidden money" etc. can cause fights, or a reason for struggle for the rest of the family. 
It depends on how you raise your child, I agree that it's better not being too transparent to them when it comes to your savings but
the only thing we are talking about here is teaching them how to manage their finances, savings and investments (if there's some) while they are still young, because there is a great possibility that once they know how to properly handle their money, they will no longer be dependent on their parents when the time came when they were getting old. Most people from South East Asian countries, even though the children are of legal age, they still depend on their parents and do not know how to handle their own money and income, so there are instances where the parents are also in charge in everything because their child is in the right and legal age already but all decisions in life of them still depend on their parents. You said, We don't know when we will die or disappear from their company, so it is better to do it while they are young and when they think everything about it, they will learn as early as now.