Facebook Inc.’s plan for a new cryptocurrency has the potential to change entire industries. A more likely outcome is that the technology transforms the social media giant’s own business.

While Facebook makes most of its revenue from advertising, Chief Executive Officer Mark Zuckerberg says the future is private messaging. That’s a tough venue for data-hungry digital ads, so Wall Street has been wondering how the company will make money from this new future. Libra, the crypto coin Facebook announced last...