If you want to initiate transactions in the financial system, you have to work through what happens when things go wrong, and be prepared, financially and operationally, to handle them. How does the money get from the parent's account to the kid's account? Note that if the kid can get cash out, you can't fund this with a credit card. Visa and MasterCard don't let you buy money with a credit card; that's too fraud-prone.
So, as someone pointed out, you're back to ACH debits. Getting set up for those is hard, for good reasons. It gives you a connection to other people's bank accounts. So you need financial strength, bonding, and good references.
Note that the chore list has to be secure, too. Otherwise the kid can add "Mow lawn, $1000", check off the item, and drain the parent's account.
If you try to do this by having the parent transfer money to you in advance, and you then release it to the kid later, you're now a depository institution. In most states, you have to be a bank or a money transmitter to do that. (It's so tempting to take the money and run, and that's happened enough times that such businesses are regulated.) Also, that's a pain for the parent. They might as well use Venmo.
PayPal was successful partly because, back when they were above the bike shop on University Avenue in Palo Alto, they started as a security token maker. So they had security people and were familiar with the problems. A big portion of PayPal's operating costs come from dealing with fraud. The legit transactions are fully automated; the problems require a big call center.