It’s still very damn useful as a metaphoric concept, at least!
Many of our common-sense sets do not have sharp edges. I mentioned the set of “chairs” in another thread. The central core of the set is obvious: office chairs and kitchen chairs and big overstuffed living room chairs. But farther out toward the boundaries of the set, the definitions are fuzzy. Is a chaise-longue a “chair?” Is a “rocking chair” a chair? How wide, exactly, does a “chair” get before it becomes a sofa?
And then there’s the real fringes: a wooden box with a cushion on top. Or (garish image!) a person on hands-and-knees, upon whom one might sit. Or a bar stool, with the seat removed: just a pylon. You could sit on top of it. (Most uncomfortably.)
The idea of sets having “fuzzy boundaries” makes for a topology that more accurately reflects the way our language treats objects. The traditional Venn topology – an item either is or is not inside the set – doesn’t work as well in a universe full of gradations and spectra.