@Daniel ******
, You may be confusing a couple of things.
Every single foreigner entering Thailand including a newborn baby NEEDS a visa except foreigners with permanent residence. And even minors also need to apply for extensions to stay longer than the entry stamp. All visa and extension fee is the same for everyone regardless the age.
Foreigner including children staying exceeding the current stamp means he is on overstay, i.e. staying in Thailand illegally.
What is waived for minors is the penalty for overstaying. Under 15 y.o. wouldn't be fined for overstaying, and under 18 y.o. wouldn't be blacklisted for overstaying. This doesn't make minors skip getting an overstay stamp. And once a child goes on overstay, they cannot be back to legal stay without leaving Thailand.
It's your decision on how you deal with your children's status in Thailand.