1. Core apps vs. combo apps
My theory goes like this: iOS started as a super early adopter device and the core apps (phone, contacts, email, calendar, etc) were simply a logical step from similar applications that have existed on smartphones for a long time, arguably with a nicer UI.
Fast forward 6 years and the iPhone brand has sold over half billion devices with an additional 200m iPads. The core apps have barely evolved compared to what has happened to the apps that are present in the App Store. There has been significant improvement in the default iOS UX but that’s just a pretty overlay on top of the same actions .
By catering to a mass market Apple has left plenty of space for app developers to take hold in their core apps.
Have replaced most core apps the latest being Humin that replaced the Phone app. Wish there was an alternative for Music
Humin really blew my mind and was looking at the common theme behind me using Sunrise, Gmail etc instead of the old ones and the answer is about combos. 
2. Enter the combo apps
A combo app is an app that aggregates data from different applications to perform its functions, and then adds a layer of intelligence/context over it to figure out meaning from this data.
With an installed base of up to 700m the mass market is interested in basic simple usability so Apple can reach people like my parents (who get a brain aneurysm every time they have to perform a new action in software that they have not done before). This creates a race to the bottom in terms of features and leave ample space for innovation to cater to early adopters who have plenty of apps rich with data already installed on their phones.
An early example was Sparrow that would use Dropbox for storage. Most apps can now connect to Facebook, Twitter and Linkedin. Citymapper connects with Hailo, Google Maps uses Uber, Gmail uses Google Drive (whatever that is), Moves is used by all health apps and vice versa. The list is long.
What this means is that you can infer additional context form past use behavior. For example you can mine emails and FB to figure out who are your closest friends. Humin automatically filters your contacts by your current location, and then (correctly) assume that you are more likely to call people in SF when you are in SF (and additionally when it’s daytime in SF) apart from the ones you marked as favorites that are always present.
And the more these apps can be connected and the more data can be harvested from each other new forms of service can be provided to the user.
Enterprise communications (whether IM or videoconference) still suck. Photo management blows as we never imagined we could have so many photos. Contacts are a mess (maybe Humin will prevail and fix this), Pocket is not yet fully integrated in other apps or in iOS. Moving unstructured data from one device to another is still a Wagnerian nightmare.
Moreover with HealthKit you are going to have a new dimension of data as well where you can link biological responses to actions and again down the road you could infer the status of a person when certain actions are taken, cluster them and build a predictive model on top.
My final point is that core apps represent the biggest opportunity. Samwer famously wrote: “there are only 3 areas in ecommerce to build billion dollar business: Amazon, Zappos and furniture” and I believe there is an analogy in mobile. Only here we are talking about a twenty fucking billion dollar opportunity  for those lucky ones that can replace a core app and build a business on.
TL;DR: combo apps are the future and you have plenty of shitty iOS apps (Yahoo! Stocks , Clock, communications) that you can re-invent. The combo can also create new class of apps that we have not discovered yet (fucking/dating/marrying, professional services, freecycling, knowledge dissemination and tutoring. The list can be pretty long.) Replace one core app and your company will be bigger than Iceland’s GDP.
PS. this idea of leveraging existing data and manipulating it and presenting it in new ways is nothing new. Y Combinator and 500 startups rely heavily on this theory while choosing their investments. Dropbox and Airbnb are prime examples. Neither requires a data entry sales force to populate or maintain any dataset so it’s enormously scalable and easy to kickstart at the same time.
 Apple has put effort where leverage is. So focus was (correctly IMO) in improving developer tools to make and sell apps rather than say improve the phone app which might be irrelevant in 5 years.
 Yes, I do have Dylan on speed dial ahead of my family. Don’t ask. It’s got something to do with Batman anyway.
 Whatsapp, I’m looking at you, without even a desktop app.
 Yahoo! Stocks. I can’t believe that SUCH A BUG-INFESTED TURD has been allowed to be on the default page of iOS and every other alternative has been built with the same shitty idea that people want a fucking Bloomberg terminal on their phone with the same fucking usability of a fucking Bloomberg terminal (hello ’90s!)