I'm sure this has been posted before, but before we know it WWDC 19 will be upon us, and I have a feeling that iOS 13 will be a huge upgrade. In a way, it sort of HAS to be, with their plateau of hardware sales. Especially for the iPad, a revamped, more powerful iOS will prompt more people to buy the tablet, especially the Pro models.
For both iPhone and iPad, I think there will be a revamped home screen at least in style. I would love if iOS icons now looked like macOS. And if we could not have to arrange everything in a grid, that would be amazing too. This would especially be great for the iPad.
For iPhone specifically, I think they essentially need to bring iPad functions of today to our mobile phones. Split screen apps, maybe even in PiP for newer and/or bigger models. Allow for a carousel of apps in the dock, not just the limit of 4. And allow for the dock to be dragged up from anywhere so you could switch to these apps at any time. I think the gen X phones could def take advantage of that with their longer screens.
For iPad, just give it the software it deserves!! Multiple windows/tabs with an app, TRACKPAD FUNCTIONALITY, a better Files system (I don't HATE the current system, but it can be improved for sure), and completely resizeable windows. I'm not opposed to iPad breaking off altogether to a "padOS" kind of deal, but I'm trying to keep this post within the realms of possibility lol, and at this point if they haven't already I really don't think it's going to happen. But, say they do... this would entice developers to create iPad apps specifically for the tablet, as opposed to just blowing up the iPhone version. I know, not all developers do that and respect the iPad, but too many of them nowadays just stretch the iPhone version for the larger screen and it's really annoying.
Anyway, those are my ideas and thoughts. Feel free to add ideas and functions I missed that you'd like to see