Even in your particular hypothetical, it's still not the best way to minimize liability or culpability.

The lockbox is fire-safe

Fire safes rarely survive actual house fires, they're typically only rated to last 30min to an hour of exposure. In the event of an actual fire, it's pretty doubtful that you'd be able to even find the safe afterwards. If it is recoverable, it's going to be found by investigators, who will probably question why you have so much cash.

their home has extensive security.

Pretty much all security is theater unless it's an armed human, and I doubt you're going to have an armed guard available 24/7.

With the business they’re doing, their government is not finding out. If so, there are much, much bigger worries than taxation.

Right, but do you know how many fraudulent organizations get busted because of tax evasion? The goal is to separate the money (evidence) from you as much as possible. Having it sit in a secured safe that only you have access is evidence makes you culpable to the crime.

the average person though, I agree with you.

I would say anything that applies to the average person applies even moreso to a person engaged in less than legal businesses.