The idea would be to share the clipboard between mac and iOS, and have a "clipboard keyboard" on iOS, so in an app, I can easily access my favorite clips and paste them (at least for text ones)

Obviously, this would be even better if you could have different "paste lists" where I can "pin" some of my clips to a given list, and select which list I want in the keyboard

That's how other "shared clipboard" apps work (at least Copy'Em, etc)