I did the exact same thing. Took me 10 minutes at the drive-up window at my bank to open a new account and another 5 minutes when I got home to link it to eBay. I don't expect to save a damn dime on fees and such but I'll admit the whole thing was easier to do than I thought.
Good point about PayPal! I've had my eBay account since 1999 (back when it was practically the Wild West - no credit cards or confirmations necessary to start an account, sending checks as payment was common, and you could leave anybody feedback for any reason ) and my PayPal account since maybe 2002, with nary a security issue from either one of them, ever. Clearly I still don't trust eBay enough to link my main bank account but at some point I have to give them credit where it's due