A tussle this week between prominent investors and Apple Inc. over iPhone use by young people comes amid a nascent re-evaluation of the smartphone’s social consequences within the industry that spawned it.

The smartphone has fueled much of Silicon Valley’s soaring profits over the past decade, enriching companies in sectors from social media to games to payments. But over the past year or so, a number of prominent industry figures have voiced concerns about the downsides of the technology’s ubiquity.

They include Apple executives who helped create the iPhone and now express misgivings about how smartphones monopolize attention, as well as early investors and executives in Facebook Inc. who worry about social media’s tendency to consume ever more user time, in part by pushing controversial content.

Those are the kinds of concerns spotlighted in a letter to Apple on Saturday from Jana Partners LLC and the California State Teachers’ Retirement System, or Calstrs, which control about $2 billion of Apple shares. The letter urged the tech giant to develop new software tools that would help parents control and limit phone use more easily, and to study the impact of overuse on mental health.

On Monday, Tony Fadell, a former senior Apple hardware executive involved in the iPhone’s creation, also called on Apple to do more, saying on Twitter that adults are struggling just as much as children with smartphone overuse. Mr. Fadell, who started publicly voicing concerns about smartphones last spring, said Apple and Alphabet Inc.’s Google should add features to their mobile-phone operating systems to allow people to track device usage.