IMO, there is a security risk in having large amounts of cash in a checking account with online access, paper checks with account numbers on them, debit cards etc...
I opened a savings account at my bank with NO ONLINE access, with no debit cards, a few checks that are stored safely (no cashed checks rolling around with account numbers on them). When I have large amounts of cash I store it in this "hidden from the online world" savings account and transfer money to checking/investment accounts as needed.
I recently called a bank to transfer funds from one account to another and the rep on the phone said they needed verify that it was me on the phone, they asked me for a phone number they could send a secret code to. THEY ASKED ME FOR A PHONE NUMBER!!! I could have been anyone and given them any phone number. I asked how this caller provided phone number verification process adds any security at all, no answer given, it was like asking your pet cat to explain banking. I gave them a phone number I know they do not have on file, they sent the code to that phone number no problem. The companies that we entrust our stash to are sometimes/often incompetent.