I hate to break this to you, but they can already buy things in physical stores.
And if you legitimately have a $20 bill, I can walk into a store, represent that it's mine, and buy things with it, never encountering an obstacle along the way. That's the same fraud you're worried about in prepaid cards.
Of course they can, but as a parent, I find it easier to supervise their store purchases than their online purchases, because they have to physically go there, and I can notice it.
Frankly, if you're that interested in tracking what your children have and haven't bought, online purchases are likely to be easier, in that they come to your home through the mail.
The general categories of things that children are commonly restricted from buying:
- Drugs. These are all black market, so availability of prepaid cards is unlikely to change how they're bought.
- Alcohol. I've never tried to buy this online; I know eBay Now wanted to sell it and concluded that the cost of legal compliance was too high. Even assuming they could find mail-order booze, it would arrive in the mail, easily detectible.
- Pornography. This can be consumed directly on the computer, raising possible detection issues. However, if you're afraid of children buying it over the internet, I've got some very bad news for you...
I also wish the limitations would disappear, but there are two reasons keeping them in place:
1) Government wants to ensure it can track all digital transfers (many pre-paid cards require activating with SSN)
2) Failing to approve certain transactions is the equivalent of a financial firewall because banks and payment processors know they haven't hardened their servers enough to prevent another one of these: http://www.nytimes.com/2013/05/10/nyregion/eight-charged-in-...
Now, if policy-makers were convinced the online-children-purchases market were bigger than the drive-by-ATM fraud, we would see the rules changed tomorrow.
And if you legitimately have a $20 bill, I can walk into a store, represent that it's mine, and buy things with it, never encountering an obstacle along the way. That's the same fraud you're worried about in prepaid cards.