If I make an error, I eat it. If the banker makes an error, they eat it, or at least you have some ground to stand on.

The app for my bank account lets me view balances (and some other info), transfer funds between my subaccounts (for free), and deposit checks.

There's not functionality in there to shoot myself in the foot.

Keep trying, you'll find it.

I mean, you could transfer too much money out of the subaccount that rent/mortgage/etc. is paid out of

You are right. Most security are really depending on banks whether they operate with integrity and your relationship with them. For security get to know your banker. And I wouldn't recommend any of large banks. Local credit union and small bank with good balance sheet are better bet.