Often no member of the public does business with these corporations. E.g., a corporation set up by a celebrity to own a private home and keep her address out of public databases.
I don't think that's any kind of justification. It doesn't matter whether it's a member of the public or another business or a government agency, there should be a known person or people responsible for the actions of any company to be held responsible for breach of contracts or bad actions. All business is based on contracts of agreements, and the whole thing would entirely fall apart if no one could be held accountable for breach of contract.
There's a lot of talk about the increase in KYC for individuals setting up accounts with banks and other financial institutions for reasons of anti money laundering. And yet anonymity is still allowed (and effectively encouraged) in business ownership which could facilitate far greater amounts of money laundering more easily.
Ever since reading about Mossack Fonseca it has bothered me (not confused me though, since the rules are made by the people who most benefit from it).
That rather misses the point. The entire reason we have corporations is to abstract those issues away. For most routine business it's better to deal with a faceless corporation instead of trying to personalize everything. The corporation itself can be held accountable for contract compliance and in extreme cases you can get a court order to seize corporate assets; that's much easier than trying to seize and auction off the CEO's personal art collection or whatever.
My understanding is that Board members are intended to be personally responsible for actions of the company.
Which is why homeless people and ne'er-do-wells get paid $10 to sign a piece of paper (which remains unread) but states this responsibility for shell companies X, Y, and Z.
Also, by design, shell companies don't tend to have assets worth seizing.
Your understanding is mostly wrong under US federal and state law. Generally Board members are not personally liable for corporate debts. It is only possible to pierce the corporate veil in unusual situations, like if they engaged in criminal activity or illegally tried to put corporate assets into their own names in an attempt to hide those from creditors or violate a court order.
I know I'm mixing up limited understandings of Australian and US legislation, and sprinkling on top of that my frustrations with those two fairly strict legislative countries allowing business to be conducted with organisations that have opaque, international ownership structures. It's a glaring hypocrisy (that I'm likely missing a fair bit of nuance due to only a surface understanding) given the ratcheting up of the surveillance state on individuals.
The whole area is something that I would like to gonzo-research as a retirement project.