The problem comes from the governments as they are financially incentivizing bankers, or whatever employee with access to sensitive data, to snitch on their customers, and directly play that information to the governments.
That's definitely true, but I think the percentage of people on purposely hiding a part of their wealth at x bank or financial institution, are a far minority. In most cases people, and then mainly referring to wealthier entities, don't have much problems with paying tax as long as the rewards greatly exceed that what they end up having to pay. I personally don't see the value of people trying to hide a large portion of their wealth outside the country through centralized financial institutions. At some point you'll get noticed where you will be forced to pay a hefty fine, plus the tax you 'owe' the government. It's not worth it.