It's not a "rule," it's just a matter of style. So, it's a guideline that can vary from one style guide to another.
It's also far from an old-fashioned guideline.
From The Chicago Manual of Style (17th ed.), 6.60:
When items in a series themselves contain internal punctuation, separating the items with semicolons can aid clarity. If ambiguity seems unlikely, commas may be used instead . . . Note that when a sentence continues beyond a series (as in the third example), no additional semicolon is required.
The membership of the international commission was as follows: France, 4; Germany, 5; Great Britain, 1; Italy, 3; United States, 7.
The defendant, in an attempt to mitigate his sentence, pleaded that he had recently, on doctor’s orders, gone off his medications; that his car—which, incidentally, he had won in the late 1970s on Let’s Make a Deal—had spontaneously caught fire; and that he had not eaten for several days.
Marilynn, Sunita, and Jared, research assistants; Carlos, programming consultant; and Carol, audiovisual editor, provided support and prepared these materials for publication.
She decided to buy three watches—an atomic watch for travel within the United States, a solar-powered, water-resistant quartz for international travel, and an expensive self-winding model for special occasions.