Unfortunately I believe it'll be a LONG time before the app can ever replace OneNote 2016. I'm an evangelist at work--I actually give trainings on it--and nearly all the functionality I highlight feature-wise simply doesn't exist in the App. I really believe you're going the WRONG way on this way. It's too bad and I guess I'll be hanging onto OneNote 2016 for as long as I can.
One thing I'd like to note--we have a LOT of OneNote notebooks in SharePoint online. When these get messed up occasionally--which happens once or twice a quarter--the only way I've found to fix them consistently is to move them to a local hard drive, delete them from the SharePoint library and then move them back to the same library. I'd be happy to talk to someone about this use case, but I don't see how cloud-only will make this better.