I think this is not a clean cut case of evil planned obsolescence. There are valid security concerns, as browsers are a common attack vector. You should get that updated, also to protect your privacy while surfing online. So for a banking site or similar, I kind of get it. (I recognize there is a possible conundrum when people can't go bank in person because the bank no longer has branches and/or get excluded by their old hardware/economic reasons from doing it online. Should they be able to choose risking it if the bank knows about a flaw they then leave exposed? Shit's complicated.)
That being said I'm sure this banner of corporate concern was not primarily motivated by the security and privacy of their users.