Well this is good news. I never owned an Apple product until my recent purchase of an iPad Mini.
I was nervous about switching from an Android tablet, but everything went great until I tried to move my home screen icons where I wanted them, and resize a weather widget the way I wanted it. Neither worked, and I had to laugh at how ridiculous it was.
I'm not sure I understand what we're talking about. When you install an app on iOS, the icon pops onto the home screen or an adjacent page if there's no room. Can you not move the icons after that? I know you can put them in folders.
At least on my iPhone (no idea if iPads are different) you can reorder, but the icons will always be "dense" meaning no free spaces between them. They will always align in full rows beginning from top left. You can put stuff in folders, and you can change the order, but not have one icon in the third row, without the first and second row being fully populated with icons.