(If they are asking my social to verify my identity, they already know it to verify against.)
Again, your personal choice could be to post you CC data on your FB wall, you're free to do whatever you want. But you're seeing this very one sided if you assume everybody should be just as comfortable with FB and anything real in their life sharing data, or relying on a 3rd party with 0 obligations towards you for those critical services.
And mind you, the problem isn't that the bank is relying on a third party for things. They may already be using a cloud service, they could also be using an Apple ID or a Microsoft account. It's that they would use a social media platform in general (thus allowing data sharing which will never do the customer any favors), and Facebook in particular (since they have some of the most atrocious morals and unreliable promises).
i agree fb is terrible at promises or treating people like they matter, but the only thing they ever do with the data collected on people is make them targetable demographics to advertisers. use an adblocker if you dont want to see them.