The problem is that the bank cannot do what you describe unless I am physically present at the bank in the flesh. If I tried it by fax, email, or snail-mail, they fear that I could deny that I ever sent the withdrawal authorization, thereby ripping Chase off.
That is what makes it irreversible. That is what makes it useful. If you want to have an irreversible transaction from your desk you need to use a bank wire.
As I implied above, the solution is not yet here, but I expect that the whole clumsy interface between slick 21st-C bitcoins, and sluggish 14th-C banking procedures will sort itself out in coming years.
There will never be another solution. Banks don't like irreversible. When hackers mass hack tens of thousands of accounts and funnel hundreds of millions in "irreversible" transactions the bank will have to eat the cost. Bank wires are the "solution". Generally users have to specifically ask for bank wire access and many banks require 2FA for online bank wires.