I'd say, let the kid play what he wants, but don't give him access to your credit card. Hell, I'd say, don't even allow any charges to your account regarding f2p, even if you kid begs and throws a tantrum. They can LIKE what they want, but when it comes to the charge, YOU hold the power and as long as YOU keep control over your bank account, you don't have to give your info to your kid. If they want it THAT bad, when they are of proper age(18 or so, I forgot how old I was when I opened my first bank account), then they are on their own. But as long as you are supplying the money, you can do whatever the hell you want with it far as your kid's concerned.
It's kinda become apparent that a lot of parents(hehe, that sounds funny) lose sight of their power and how they can control a situations when their kids are involved. Always remember, you hold the money, you hold the right as a adult(the right to consent to things that youth under the age of 18 lack) and YOU pay the bills(there for have the rights over internet and phone privileges).
That being said, a kid playing f2p without the ability to invest money into those games is harmless. Let him have his fun.