Unethical behavior? Illegal activity? It's certain that shell corporations have been used to hide these things.
I'm not saying that a person should be unable to maintain some anonymity. But I am saying that corporations should pay taxes on their income, and being entities formed specifically for certain legal standing they should not have the same right to privacy that individuals have.
So if one wants to be anonymous in one's personal activities, one should not form a corporation to conduct them.
And if one wants to be anonymous in one's business activities, one should move to another country that is more supportive of organized crime.