When Steve Jobs took a swipe at Amazon.com Inc.’s Kindle in 2009, he pointed to the online retailer’s decision not to report unit sales of its reading device as evidence it wasn’t selling many.

Nearly a decade later, Apple is following a similar path. The company said it would stop disclosing data on the number iPhones, iPads and Macs it sells, eliminating a performance metric it has provided since the 1980s.

The...