I think the thing that makes it more intuitive is that it's really easy to see how "flatMap" relates to "flatten" and "map", whereas it's not immediately obvious how "bind" relates to "join" and "map".
And I think expanding a concept which someone already comfortably understands is a lot easier than asking them to learn a new one, even if you say it's kind of similar.
And FWIW, I don't think "flatten" is particularly unintuitive name, even for the more abstract cases, because it's still f (f a) -> f a. The mental gymnastics here is understanding how a Functor can be more than just a container, and you kind of need to learn that anyway.