In the US most bank checking accounts have a monthly fee which is waived if you meet certain conditions, like maintain a minimum balance (I think mine was $1000) or get an automatic direct deposit at least 2 times per month of $250 or more - these would be hard to meet for a childs account. Credit unions are usually free though.
There is usually a "relationship waiver" that eliminates the fees on all the accounts you're party to as long as you have enough total wealth parked with that bank.