I suppose it depends which authorities you’re trying to hide money from.
I can say from my experience that if you are trying to find out the ultimate ownership of a company, hitting a jurisdiction that either doesn’t require registration of officers/members or doesn’t make the register available to the public brings you to a dead halt.
According to Mossack Fonseca at least, it doesn’t. Not if you undertake no trading activity in the US and have no US source income.
They actually go through the alleged benefits quite well in their marketing material: