This paper nicely illustrates a genre I’ve seen a few times before. Pick a problem where there’s some symmetry or feature you can exploit to speed up the calculation, do so, and then compare it to Nested Sampling which doesn’t assume that you have problem-specific insight like that. Of course, the customised thing will beat the general thing in such a case.
A reductio ad absurdum of this kind of paper is to present a problem where you already know the answer. Then, the proposed method of already knowing the answer will be infinitely computationally more efficient than Nested Sampling, or indeed anything involving a computer.