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.
Why, if you're searching for symptom X, would you want to find emails with X, text messages with X, and that image which just happens to contain X in its filename?
You could very well want any of those things searchable for symptom X if the email, text message, or Image has relevant details for symptom X. Perhaps the image is an X-ray, the email is a diagnosis from a colleague, or the text message is relevant data about the diagnosis. The very fact that you think they should have to load 3+ different apps to find all the data relevant for symptom X or purchase a high priced propietary app that somehow bundles email, imaging, documents and sms all into one interface shows a lack of vision. Just because every medical device in the field works that way doesn't mean it should.Know of a search API which properly handles (every possible use of) context? Without that, people distrust searching because of irrelevant results. Google does well because of PageRank; as far as I'm aware, nobody has arbitrary-context searching which is effective, because it's such a ridiculously complex and/or processing-intensive problem. Such a filter would probably be integral to passing the Turing test, so we'd probably have heard of it if it existed.
The context space is much smaller on a device like a phone and it's quite possible to craft a query that finds what you need faster than finding the app, opening it finding the search option then typing it in.
On my Android phone I love the search feature. It's a lot like having quicksilver on my phone. A single button that gets me access to everything.
I may very well be inflating things, but the instant you mention "craft a query" you've lost 99% of people, minimum. They'll type "lupus", and give up if they don't find what they want. Or "Tom", and stop trying if they don't find Greg and Lupus as well. And then resort to finding the information through whatever roundabout means they last succeeded in.
Beware the average user's depth of knowledge of your system; many don't understand how to use tabbed browsing, and possibly more use Google to find the Facebook login page despite the login link appearing at all times when you're logged out. If you're trying to get as many people as possible, you've gotta plan for the bottom to be as functional as possible. And there are more at the bottom than at the top.