Download the Documents app by Readdle. It's free and is the file directory / finder iOS is missing. It's integration with share sheets kicks ass. I love using its built in browser with video downloader webpages to collect youtube videos and store them on my ipad for the kids.
And to OP, I think these proposed features are too complicated. Three finger drag down to get to a shelf thats basically a multi-clipboard is awkward and leads to shelf-rot - hundreds of ****** clips sitting on the shelf... then we get shelf search in iOS12? Eww. And drag drop is interesting, but not that much different than the copy paste between apps that is already implemented.
Requiring all apps to support landscape mode would be where I would start. It's super frustrating to rotate the screen to realize the app doesn't support it - and just lazy by developers these days.
Context aware and conversational siri would be number two for me. She doesn't understand what I'm saying half the time and is very limited in what she can do. Sometimes I want her to read the email I have on screen (read this email) or help me get to my content faster (find the email from Bob about Cancun) or (show me the last email from Andy) or (add Bob, Liz, and Sam to this email). I feel like Siri is missing thousands of canned actions. This is especially annoying when the text on screen shows that she understands you, but that action has not been defined in her "brain". I'm always surprised by what she can't do, and rarely suprised by what she can.
Split screen improvement would be my third. I should be able to keep pulling splits from the right side. I should also be able to pull a split from the top or bottom of the screen, or an already split panel. I should also be able to rotate a split pane to any angle I want. Mini icons on the split pane to change the split app being viewed would be really cool too. The split view app switcher is super awkward right now.
I agree with this video on the denser icons and multiple audio streams. Often I want to be listening to music in the background while I'm watching a tutorial in split screen.
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I feel like a broken record, but the Documents app by Readdle does all this.
OK I'm going to have to grab this, thanks!!