my kids are now 14 and 11. Neither one has a bank account. Every gift event their great grandmother (Wife's grandmother) writes them a check made out to them. We have asked her to just write the checks out to us if she insists on doing checks but still get the checks made out to the kids 2-3 times a year.
Thankfully my bank doesn't seem to care about depositing them.
My kids are currently 10 and 14. They've had bank accounts of one form or another for over 5 years now.
Started out with some virtual bank geared toward children where the parents open an account then create sub-accounts for each kid. Then you can setup scheduled transfers for allowance, and create "chore lists" where they can earn extra money. They each had a bank card they could use and a phone app they could check balances/transactions. Worked well, but was a pain to transfer money into from our regular bank.
Once we moved, we set them up with accounts at the local credit union. Similar setup, with the parents having a master account, and sub-accounts for each child (both chequing for daily use and savings that's not linked to the debit card). Scheduled transfer happen each week for their allowance. And we make them put 10-15% of any extra money they receive (gifts, work, etc) into their savings. When their savings gets above $500 then we roll it into a 1-year GIC since the actual interest on a savings account is virtually 0.
They do their own deposits into the bank. They do their own budgeting/saving for things they want to buy. They do their own shopping for Christmas/birthday presents (we do help with that if there's something they want to get that's more than they've saved). And they pay for all their own slushes, ice cream, movie tickets (for shows they want to go to without us; shows we take them to we pay for), etc.
The youngest was very much a saver, considering herself to be "broke" if the chequing account dropped below $100, while the oldest was very much as spender, rarely having more than $10 at any time.

Lately, the oldest is getting to be better at saving up for things and looking beyond what she can buy today.

The youngest still sets up their iced tea stand outside our house every other weekend or so, selling drinks and bracelets, rings, and necklaces they've crafted.
Many of their friends at school don't have bank accounts, though, which seems weird to me.
I had my first bank account before I was 6. Managed to save enough money to spend my 7th birthday on a cruise ship coming home from Disneyland (yes, my mom paid for most of it, but I still contributed $400 which was a lot back in the early 80s).