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To be pedantic, this is not really a jigsaw puzzle, the pieces are squares, I'm guessing the technique may be applicable to real jigsaw puzzles, too.

I'd like to see this applied to puzzles with unique pieces like the ones here (https://libertypuzzles.com/about)

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I thought the same thing when I saw it, but I think this just makes it a more challenging problem. You don't get the constraints of edge and corner pieces to start. There is no confirmation of fit with unique interfaces. When every piece is equally interchangeable the problem is more difficult from a human perspective.

Although, from a computer perspective it also makes the edge comparisons nice and clean.

But in case of square puzzles their orientation and border match is limited

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