Once you're on non-antique Windows, there's nothing preventing you from going all the way to IE10 which, again, starts getting into situations where not upgrading for security reasons starts approaching negligence.
But Vista and 7 do not, and you can can run IE8 on them just fine. IE8 itself is supported as long as Windows 7 is, which is Janurary 2020 for the extended support phase.
> Once you're on non-antique Windows, there's nothing preventing you from going all the way to IE10
Nothing. Nothing at all. Unless you consider a large collection of legacy applications that either just plain don't work in anything other than legacy IE or simply haven't been tested (and signed-off as compatible and SLA-covered by the supplier) in anything else.
They can't take the risk of not getting getting those apps thoroughly tested before upgrading and that will cost money (as will any changes, or complete replacemets, needed) and more importantly a huge amount of time (nothing moves quickly inside a bank no matter how hard enthustic and/or concerned people push - organisations of that size have trouble working up the inertia for significant internal changes).
My suggestion has always been to install something else alongside IE and migrate that way: keeping IE around for those applications that require it (or have not been signed-off as working well on something else) but having something better for applications that don't rely on "classic" IE's excetricities. I get funny looks for that suggestion though - the thought of training users to cope with two programs where they once had one seems to trike TS people cold.
> approaching negligence
One of the key drivers working against building up change inertia is fear of neglidence (or accusations there-of). Large organisations have a significan aversion to risk, organisations within regulated industries (where you may do more than fail: you may fail and pick up a hefty fine and/or loss of license along the way) in particular, if they were people you'd probably call them neurotic on the matter. Change without sufficient plannig is a form of negligence, and fear of this is a large part of what adds friction to any forward movement.