If your bank leaks data, you would be in so much trouble that thinking about privacy implications of that would be pretty low on your list.
That's just your bank. If a global payment processor like Visa would leak data, there probably would be ripples going through most financial system (i.e. whole countries abandoning it, etc).
This makes zero sense. The biggest trouble is with the data/privacy, the funds would be safe. And no, the world wouldn't stop because of it, pretty much the opposite, small/medium scale leaks happen quite often and big ones aren't unheard of: https://m.startribune.com/target-settles-visa-card-issuer-cl...
Your entire digital life could be stolen from you if someone knows your name, address, DOB, and last 4 digits on your card. Attacker can go through e.g. the Gmail password recovery process very convincingly impersonating you.
Gmail will let someone who has that information take over your email account?
The name+address+DOB of many people are public. So anybody who gets a glimpse at someones "card" (I guess you mean credit card?) would be able to take over their gmail? That would surprise me.
