Last week I needed to make a highly time-sensitive transfer of ~20k that had to clear the same day. Chase charged me a flat fee of $25 for the wire (and Ally Bank would have been happy to do it for $20). Chase temporarily froze my account since the payment was so large it was immediately flagged, but I spoke to someone on the phone within a few minutes, verified it was all legitimate, and the transfer was then processed without issue.
I fail to see how Bitcoin could have helped any of this.