Arbitrary swizzles both in the forward permute (currently in AVX512) and backwards direction (GPU only) is as necessary and proper as gather + scatter. Any program that uses one is highly likely to use the other.
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Butterfly permutes should be especially accelerated, as that pattern continues to show up. It seems like arbitrary permutes / bpermutes are expensive to implement in hardware, but butterfly permutes are the fundamental building block.
Butterfly permutes are needed from FFT to scan/prefix sum operations. It's also fundamental (and simpler at the hardware level than arbitrary bpermute/permute)
AMD implements the butterfly permute in DPP instructions. NVidia provides a simple shfl.bfly PTX instruction.
Butterfly networks (and inverse butterfly) are how pdep and pext are implemented under the hood. http://palms.ee.princeton.edu/PALMSopen/hilewitz06FastBitCom...
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IIRC,the butterfly / inverse butterfly network can implement any arbitrary permute in just log2(n) steps.