Lean Thinking Needed

Bank Wire Transfers vs. FedEx Delivery

My goal was to give them all the paperwork, ensure I had sufficient funds, and schedule the transfer such that the money arrives in the sellers' account on a particular date next week.

But they can't do that. They cannot hold the paperwork for any amount of time. They'll process it the same day I turn it in. I guess I can understand that. They're a bank, not a scheduling service.

However, they can't tell me which day to drop of the paperwork to ensure that the funds arrive on my target date. The teller informed me that "it usually takes 48 hours, but that doesn't mean the funds will be available on the other end."
...
I can get a FedEx envelope, stuff it with $100 bills (or a certified bank check), and send it overnight with a signature required for less than $30 (without insurance). In this scenario, I get to track the progress of my package remotely and am fairly certain that it will arrive on the right day.

It seems to me that FedEx is better at what ought to be a core competency of an organization like Bank of America.

It seems to me a bank that can't do better than this should be embarrassed. They need read management improvement articles or Lean Solutions and start delivering decent service or let someone else manage the company.