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In the article by Kosterlitz and Thouless (1973) they write in the abstract: "This type of phase transition (BKT) cannot occur in a superconductor for reasons that are given". Later in the paper they say that their argument for the BKT transition cannot be carried through because the singularities in the superconductor is finite.

I do understand why their argument doesn't work for superconductors. However, I feel like their conclusion of disregarding a BKT transition is too strong.

Without fully understanding it, https://en.wikipedia.org/wiki/Superconductor_Insulator_Transition seems to suggest there is a BKT transition for superconductors.

Now I don't know what to believe, and I would appreciate any clarification! I would be especially interested in the 2 dimensional case.

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I found the same statement puzzling given more contemporary discourse. Tony Leggett provides an explanation for this in his lecture notes on 2D materials (https://courses.physics.illinois.edu/phys598PTD/fa2013/L12.pdf), with the argument of enhancement of the London penetration depth in very thin (and dirty) films, and the renormalization of long-range behaviour of the vortex-antivortex interaction, as well as the supercurrent around the vortex. He demonstrates there that something very similar to the neutral superfluid can be recovered.

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