Essentially every laptop / tablet / whatever-PC in use in the medical field works similarly - they use one application which handles all relevant data, and it doesn't search outside that. And this is on a PC, which is essentially wide open to application interoperability (if not as easy to do). Developers and users have already apparently decided that it's not as important / desirable as many would like to believe.
Granted, there are cases where this is useful, but it's a fundamental iOS / Android(/Unix) design choice. Android favors interoperation through APIs, iOS favors using one application for the job at hand.