Thank you for the non-downvote. :)
As far as I know, what you propose would have to mean hosting the main site on one server, and the banking site on a different server, as you cannot assign different cipher suites on a per site basis, only at server level.
Now this is not a bad idea at all, but it does mean that again, anyone connecting to the banking site would be required to have a browser and operating system that supported the latest ciphers, or the connection would fail. So really no different in outcome to what we have already.