Much like a three-years-old should not have an ability to light matches, or push a screwdriver into a power socket, or operate a chainsaw.
It sounds like many games are set up to 1) encourage you to enter account information at some point and 2) not make it obvious when you are going to spend more "real" money.
Obviously these situations could be avoided in various ways, but I think it's being pretty hard on parents of young kids to blame them entirely for "falling for" scenarios that are pretty dodgy. Especially if you are a) a technologist of some sort and b) don't have kids, I would really think carefully before deciding the parents are 100% at fault.
I see how being a parent of a young and active kid can be exasperating. But, if anything, it should increase the level of healthy paranoia :)
Am I the only one that is impressed by a 3 year old knowing how to use a credit card online. I have trouble, at times, getting all 16 digits correct--depending on the past week's workload.
I have less sympathy for the high-school and college kids who did this.