Numbers 2, 3, and 4 are the result of a powerful static type system, purity, and having typed IO. Nothing you listed has anything to do with being a monad. They're just examples of things you can do with types.
Your numbers 5 and 6 are sort of accurate. It's true that you can say "Hey, I think this type might form a monad," and explore from there. But if it does, it's nothing greatly interesting - you just get to take advantage of a bunch of existing library code. (And a little syntactic sugar, in Haskell.)
Right, my presentation is clear that it's not just monads, but rather the interaction of purity, strong types, and monads that gets us those benefits. I list them when people ask about monads because, while they might not be what monads are actually about, they were big things that Haskell gained with the introduction of monads. So I think they're an important part of the explanation that we give to Haskell newcomers.
Numbers 2, 3, and 4 are the result of a powerful static type system, purity, and having typed IO. Nothing you listed has anything to do with being a monad. They're just examples of things you can do with types.
Your numbers 5 and 6 are sort of accurate. It's true that you can say "Hey, I think this type might form a monad," and explore from there. But if it does, it's nothing greatly interesting - you just get to take advantage of a bunch of existing library code. (And a little syntactic sugar, in Haskell.)