Well, that depends on how you define "the Great Filter" I suppose. For many it's attempting to explain why intelligent civilizations are rare, rather than why Kardashev type 2+ civilizations are rare. Of course, if you strictly define it as "the thing that makes it look like intelligent civilizations are rare" I guess that would also work... I just rarely get the impression that this is what people are referring to.
I see. Well, we cannot say whether life or intelligent life is rare. There could be millions of worlds with civilizations like ours and it wouldn't be that strange we missed it.
However, it does seem that the Milky Way is not collonised (not even the other galaxies as far as we can tell), and if that's truly the case, then it would suggest that there is some kind of filter barring all civilizations from ever doing it.
I consider interstellar travel not ever being viable a legitimate filter.
Of course there is a plethora of other solutions as well.
I think you are in fact laundering the very large assumption you're making.