The stupid part is they don't stop their websites from working on desktops when they detect it's being accessed with an administrative account.
If it was such a useful and important feature then why don't they all do it? In fact it seems it's mostly small time banks that do this. Most of the major ones I've used don't seem to care at all to even attempt to detect it (Capital One, BofA) or if they do, they just display an easily dismissible warning (USAA)
This tells me that this "important security feature" is just very low hanging fruit for smaller banks to pick so they can say they have good security with minimal investment. It's about as useful as that "unable to pick your own username" security thing I mentioned (which also seems to be only a smaller bank thing)