Since iPhone exists, it looks like this:
iPhone has always been rectangular with rounded corners and a circle at bottom-center. Nor the placement or the shape of the home button, neither its functionality has changed in its lifetime. To change any of them means a lot of headache. So, I am pretty sceptic, if Apple would ever alter it. At least, any time soon... 
At this point, I rejected the idea to adopt the Touch bar of the MacBook Pro. It would always be clashing with the Home button. If the Home button were replaced by the Touch bar, there would be no way to close the apps. If the Home button was at the same place, scattering the function buttons around it, sounds crazy. Neither the last option would work: to move the Home button toward the left or right side of the screen. Should the user really need to hunt for it? Nope. 
Studying the recent acquisitions by Apple, I became suspicious. Face and emotion recognition, connecting the real world with digital content, big data and machine learning. Any of them separately would create a better iOS, but what if they were merged into one big something? Let say, into Siri? If the rumors are true, more powerful hardware is on the way, which supports augmented reality (AR) smoothly in 4K resolution. Do you get the idea?
My bet for Apple’s next big hit, is a new Siri with augmented reality support. 
This also helped me to find out how to use the liberated space around the digital Home button. It’s the gateway to Siri AR! Let me explain it. 
The real world is not hidden by the device anymore. If raised, the environment is visible in the background of the home screen in a semi-transparent way, indicating that you can unveil it by pressing the digital Home button. Same way as now, but Siri would be present in augmented reality. 
Siri would now not only listen you, but would see the world. It would recognize objects, know where you are, what your activity is and what you probably need in that moment. 
Do you see the application icons next to the Home button? Those are smartly selected functions by Siri that might come handy in that situation. Since SiriKit exists, it seems logical to do the same with AR as well. The space around the Home button is perfect to present the augmented reality related functions, let’s name it AR widgets. 
Siri is becoming a more clever conversational partner, so it can understand contextual questions easily. 
“Hey Siri, what’s that tower?”
The cards from relevant applications give you handy options, but it’s even better if you just keep on with the conversation. 
“Siri, guide me there”
It is a lot easier to follow the directions and the digital path if it is projected on the environment. 
Siri would not direct you through Europe, when you want to go to Coit Tower from Russian Hill. I know, I went far from San Francisco with this example. I’ll go even further with the next idea. 
“How is Sandra?”
Wouldn’t it be great if you could get health data about yourself and your loved ones so easily? Obviously, sharing those data is synced among iCloud Family, so those who have older iPhones, could also enjoy this experience. 
iPhone 7 vs iPhone X Concept
In the case of an edge-to-edge screen, the Home screen would also need some change. The reachability of the top icons is hard even on an iPhone 7. It’s not a good idea to move them up even more. However, aligning them to the bottom would be a pretty good move. 
Note, that the bottom part of both the iPhone 7 and iPhone X concept is almost the same. I think, it’s important for the easy adoption of the new technology.
How an app would look like?
The augmented reality features would not only be accessible through Siri, but in all apps - if they have AR widget. For example, Facebook got a Friends Near Me and a Live AR widget - the latter lets you follow an event by different view angles, on the spot. 
Although this concept is only fantasy, I took the aspect of developers into consideration. 
Firstly, I guess they wouldn’t welcome the new screen size so warmly as the consumers. This concept is based on the iPhone 7 (750×1334 px) resolution. In my own non-engineer way, I calculated the new screen resolution as 832×1744 px. The Home button panel takes 192 px in height, but the status bar remains the same 40px. However, due to the placement of the camera and speaker, a further 48 px would be required above the status bar.  It means, that the application can use 832×1464 px area, which is not perfectly scalable to the existing sizes. The good news is that auto-layout would able to manage this, however, some revision would surely be ahead.  
The above mentioned camera and speaker placement probably would mean increased engineer headache and costs. My design would be rejected Jony Ive and the engineering would be cancelled by Tim Cook. Lastly, don’t forget that the edge-to-edge screen probably results in a more vulnerable device with more expensive spare parts. That wouldn’t make you happy. 
This design concept proved me that edge-to-edge screens won’t happen just because of aesthetic purposes. It can only come along with a revolutionary new feature from Apple, which fills up the whole screen with appropriate content. In this case, not the bigger display, but the new killer-feature would sell the iPhone X. 
The mockups I used provided by Love them.
The images I used found on and Cool stuff.