Well, you can say the same stuff about anything, really. You can say that, for example, the law is what makes the state possible, and creating and keeping wealth But this does not excuse a breach of attorney-client privilege. A lawyer who "blew the whistle" on a murderer would face severe penalties.
You can't just invoke the importance of the state here--you have to say why the situation is different for banking, but you only address this particular point with childish name-calling and complaints about injured feelings.
Actually, privileges are exceptions to the rule, and they each have their own justifications. The rule as stated is fine, and any privilege must be specifically justified on its own.
Attorney-client privilege and psychiatric privilege exist for different reasons. Attorney privilege comes from the necessary functioning of the judicial system, as you pointed out. Psychiatric privilege, in the opinion of the U.S. Supreme Court, "serves the public interest, since the mental health of the Nation's citizenry, no less than its physical health, is a public good of transcendent importance"
What is the reason that a banking privilege should exist? What "public good" is being served by protecting private transactions that outweighs the harm done by evasion of tax laws or other regulations? That's a difficult question to answer, and simply saying "it's the same as other privileges" is not sufficient.
Actually, a lawyer who fails to blow the whistle about a potential murder can face severe penalties. Privilege only extends to information or facts about past actions, it doesn't apply to future or ongoing circumstances, and definitely not if you're complicit in the crime.
The banking analogy would be a banker who can't reveal how much money you used to have. Current balance would not be privileged.
You can't just invoke the importance of the state here--you have to say why the situation is different for banking, but you only address this particular point with childish name-calling and complaints about injured feelings.