My experience is limited, but I consider that to be why the Continuum Hypothesis isn't very interesting. The continuum is how we try and embed "space" into ZFC,

My experience is limited, but I consider that to be why the Continuum Hypothesis isn't very interesting. The continuum is how we try and embed "space" into ZFC, but the way we embed has certain freedoms in it: one of which being the size of the set that is used to represent the continuum. It's the same kind of uninteresting as the difference between the two implementations {x, {x, y}} and {{x}, {x, y}} of the ordered pair.