Wow - you must have limited experience with children whom God has called.
I have 4 children and each one of them were saved by the time they were 7. My two older girls were quite young (5) when they came to us in different ways and wanted to be saved. They both had heard the Gospel all their lives. They had seen it lived out before them and they knew it well. They wanted to be counted as God's child and repented of their sin and believed on Him. Along came my younger two and they were the same. Heck, *I* was just 7 when I came to know Jesus. Was I a full out theologian at that point? Nope, I didn't know the whole of doctrine but I knew the Gospel and that was enough.
My children knew the cross, knew sin, knew the price of their sin, they knew of God's plan of salvation through the Old Testament to the cross. They really DID know a lot by the time they were saved because we educated them. After messages, we ask them their opinion and I can tell you that they do not fall asleep during sermons. My now 12 year old (third child) even will critique my husband's messages on the way home from church.
My two older daughters are 20 and 23 and are walking strongly with the Lord and discipling younger women. Remember, they were saved at 5 years old.
So I disagree with all you said above.