(I wouldn't call The Culture "leftist" exactly, as it seems to be a space version of liberal imperialism, which the international Left always opposed. Though it is "left" in the American Fox/CNN-tier sense.)
If I choose to believe Banks' quote, then I have to interpret The Culture as merely the best possible society, in a universe where human nature severely constrains what societies are possible. To me it seems to be a world full of pointlessness and barely-suppressed existential angst -- so perhaps he is saying: "Imagine that we can solve death and supply unlimited entertainment and pleasure. Even then, you will not be able to escape a kind of background noise, an omnipresent drone, in a minor key -- because that's inevitable to existence."
Now I imagine a back-story: The people of The Culture, the Minds, everything -- they are actually in Hell. Their universe is Hell. They are incredibly clever; they have outwitted the gods (to the extent possible); they have ended the tortures, chained Satan (or whoever used to administer), and found ways to roast marshmallows over the lakes of fire. It is a tremendous triumph. And yet they are still in Hell, and no matter the palaces they build there or the drugs they take, there is pain beneath the surface.
I read The Culture books as a subtler version of that story, where it is never spelled out clearly where they are.
At the same time, don't take this to mean that I want to force some religious meaning onto the books. My meaning is also secular. Hell is a metaphor of some kind. The meaning I am suggesting is more existentialist than religious.