My desire to finally make friends with the iPad and get some serious writing done has coincided with the release of Paste 2 for iOS. It was suggested as a Copied alternative by Evan a couple of weeks ago.
It's a free (on iOS,) clean and simple clipboard app with iCloud sync and the Mac version appears to be highly recommended, but it still frustrates me that, on the iPhone, you have to use a sharing extension, open the app or activate its widget for it to receive copied items.
Maybe the experience is better on an iPad where you can use split screen or have it as a "slide-over" app.
I still wish you could grant iOS more system level permissions (like you can on MacOS) so that this type of app could actually monitor the clipboard properly.