Anon, I had been with a bank that had a similar promotion (a long time ago). We could easily identify them 1 and 2 years later when they became inactive, then dormant. Parents are too busy to think of adding to the account.
Like Brian mentioned, " I find that minor accounts tend to be low balance and expensive to the bank to manage in terms of staff time, monthly/quarterly statements, etc."
Integrity. With it, nothing else matters. Without it, nothing else matters.