> Like transferring money to another bank. Or transferring money to another bank to an account that isn't mine.

These sound like good avenues for fraud, i.e. places where a bank would need to put in a fee so they can afford computers and people to watch for fraud when someone attempts one of these transactions.

> Or a savings account

My Simple account bears interest every month. I suspect they implemented this automagic movement of money without actually exposing it to the user.