"suppose my fiance owns properties in South Africa, which he rents out as passive income. Is he expected to sell these properties in order to qualify for a work auth? " - then, it is an investment, and no, he is not expected to dispose of his investment (real estate, or otherwise).
"There's not even any way to report these earnings to the IRS because it's literally none of their business." - The IRS will certainly be interested in your worldwide income and sources of revenue. You probably won't pay taxes, however, you do have to declare them. Same goes for assets abroad (google FBAR to get started).
"I'm neither an economist or a lawyer but I am struggling to see the drawback to make this illegal. " - No one is saying it is the most logical law and rules, and in some ways rules from one entity will contradict rules from another, however as soon as you work and receive compensation/expect to receive future compensation, while physically in the USA, is where it gets darker grey, than simply "grey area".
Best of luck to you and your family.