My iOS 10 Wishlist:
1. A moderate design refresh - Tweaked UI should take more design cues from OS X Yosemite/El Capitan: refreshed icons, buttons, less white, a bit of depth and shadowing, etc.
2. Full system dark mode: this mode would be on by default on black/space gray iOS devices but could easily be toggled with any iOS device.
3. Redesigned music app: Apple really should go back to the basics with this app as it's gotten way too bloated and some of the UI choices made in the app need to be rethought. The stock music app should basically be the simple iPod music player that we all know and love. The iPad version of the app could use some better UI for its larger displays. The Apple Music service however, should be broken up a bit. For instance: the radio features of Beats 1 and iTunes Radio could easily be it's own Pandora-esque app. They should just drop the Connect feature, nobody really uses it (artists and fans) and it didn't work before with Ping so why would it work a second time around? Insanity 101 right there. Finally, the actual music streaming should be integrated into the iTunes Store which I'll explain more in a bit. Finding and streaming music should be as simple and easy to do as buying a song or album. Basically, you would have your recommendations (For You) and curation stuff in the iTunes Store which is where you would be asked the music (the bubble interface but redesigned) that you're into and from there, the iTunes Store would be tailored to your music tastes but obviously it would still include the top charts and spotlight searching. So essentially that would be the 'New' section as it's currently displayed. To stream a song or album, you would (if you're an Apple Music subscriber) have the + option button right next to Buy button to either: Save to Music to stream only or save and locally store it as well but you could always eventually save it locally from within the Music app if you only wanted to stream first (which is good if you're unsure about the music beforehand) It was removed in iOS 7 and I don't understand why but there was an option on the upper lefthand side of the music app as well as the iTunes Store in which you could quickly jump back and forth between for quicker access so that should definitely return.
4. Social media widget in the Notification Center. Debuted in iOS 6, removed in iOS 7 (hasn't returned since) but it's still on the Mac so if OS X has it, why not iOS? Also some good Notification Center widgets that OS X has but not iOS are: iTunes Mini-player, Weather, World Clock and Calculator. Apple, please bring these widgets into the Notification Center on iOS. It would definitely be really good for the iPad.
5. Better iPad UI optimization: The UI for the iPad was much better designed and laid out prior to the iOS 7 redesign in which it essentially scaled up the iPhone UI and didn't decide to fully take advantage of the larger screen canvas. While I admit Apple has made strides in this department (bigger folders, Safari tab view, etc.), stuff like the app switcher, Spotlight Search, Siri show that Apple did not really put much thought into adapting the new iOS design language to the larger iPad displays and the next design refresh (which I hope iOS 10 is), it should be designed with both the iPhone and iPad in mind.
6. Individual stock app updates through the App Store. I hate waiting for full system updates to get refreshed default apps. The preloaded apps should be individually updated the same exact way they are on OS X and preloaded apps that were previously downloadable but are now baked in (iBooks, Podcasts, Find My Friends, etc.) are among the stock apps that could be removable. So basically, core stock apps like Phone, Messages, FaceTime, etc. cannot be removed but the secondary 1st party apps are. But all stock apps can be individually updated via the App Store.