Fairly certain that Sherry Turkle also talked about this phenomenon in Reclaiming Converstation. They cite Alone Together in the article, though, so perhaps the research's focus on the mere presence of smartphones is more novel than I thought.
This part is fascinating - I love the term 'automatic attention':
Frequently relevant stimuli, such as those associated with long-term and/or self-relevant goals, may automatically attract attention even when the goals associated with these stimuli are not active in WM (Shiffrin and Schneider 1977; Johnston and Dark 1986); for example, individuals automatically orient to the sounds of their own names in ignored audio channels (Moray 1959), and mothers, more so than nonmothers, automatically attend to infants’ emotional expressions (Thompson-Booth et al. 2014). Automatic attention generally helps individuals make the most of their limited cognitive capacity by directing attention to frequently goal-relevant stimuli without requiring these goals to be constantly kept in mind. However, automatic attention may undermine performance when an environmental stimulus is frequently relevant to an individual’s goals but currently irrelevant to the task at hand; inhibiting automatic attention—keeping attractive but task-irrelevant stimuli from interfering with the contents of consciousness—occupies attentional resources (e.g., Engle 2002).
Smartphones serve as consumers’ personal access points to all the connected world has to offer. We suggest that the increasing integration of these devices into the minutiae of daily life both reflects and creates a sense that they are frequently relevant to their owners’ goals; it lays the foundation for automatic attention.
I once read that the army considers willpower a depletable resource. Attention, really, is one way to use your willpower, and the conclusion that smartphones are an automatic attention phenomenon ergo a willpower drain makes a lot of sense to me.