It is already the case, more or less. Parents manage their children assets, including money, and children abilities to enter into contract is very limited. They can manipulate money, but only if they parents let them, and they usually do, because it would be crazy not to.

It changes nothing to the situation with ads. Ads for children actually target the parents, manipulating children so that they can in turn manipulate their parents. It can be terrible, for example by advertising for something fashionable to wear at school, too expensive for the child allowance, they expect their parents to buy it, because if they don't their kids may get bullied. Not giving children access to money won't solve this problem, quite the opposite actually, if it was their money, they could realize how overpriced the thing is and how much they could do by spending it elsewhere.