My wife has an iPhone and is able to use her Nest app at the same time I'm able to.
But we generally don't use the Nest app much any more, except to use its horrible scheduling interface (horrible because Google's UI for changing the schedule is way too finicky and non-standard).
Everyone in the house uses HomeBridge which has a fantastic Nest plugin. The plugin uses the API you mention. Much faster than opening the Nest app. Less than 1 second to update the temperature and hear the furnace kick on via the iPhone's control center.