I think Apple faces a real dilemma here. Any API that facilitates data sharing between apps without user interaction can easily be abused for tracking purposes, a practice Apple has opposed pretty strongly – at least in word if not in actual rejections of apps.
Just like ad networks, analytics services and social network companies ([through] social sharing buttons) are able to track users across websites, analytics and ad libraries can track a user’s app usage across multiple apps as long as they have a common identifier for each device. Trackers used to use the unique device identifier for this purpose until Apple forbid it. Afterwards, many libraries switched to solutions that involved shared pasteboards. I am not sure if tracking companies have found another solution that works in iOS 7 (short of heuristics).
I’ve previously focused on the user interface challenges faced by Apple when designing an inter-app sharing system. I don’t think the Share sheet is necessarily the best option, and there are edge cases which require a more comprehensive consideration of what intrer-app sharing entails. Begemann raises some smart additional concerns regarding the security of inter-app sharing.