SWIFT is the only single entity trusted by all banks in the world. I think they would be a perfect fit for a CA to issue online banking certificates, since there is no way to get around trusting SWIFT as a bank, so they might as well trust them for their certificates as well, instead of trusting Symantec or any other CA. The less entities you have to trust, the better.
Banks shouldn't be relying on outdated infrastructure providers to do things they aren't good at. The sensible thing (and indeed more or less what happens now) is for banks to choose a best-of-breed CA to issue SSL certs, the same way any other company offering sensitive services over the Internet would do it.