That has to be a BofA rule, not a general one. I recently handled a professional association meeting's cash, w/d for change and redepositing (several $100s) with added meeting receipts, and had no problem at all with the teller. Of course, that was Wells Fargo not BofA, and I've had no problem with modest (up to a few hundred) cash transactions at Chase either though that was a while back. WF does have a limitation at the ATM for depositing cash, but it's the number of bills (30 I think) not the total amount. Credit Unions never hassle me as long as the amount is within the federal limit - they're happy to have my money!

The only actual federal rule I'm aware of requiring special handling and ID for cash is the one about $10K or more in cash or negotiable securities; that's been around forever.