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I probably misunderstood, but it seems to work. "Align with edge" I meant aligning with any edge of any box which is already in play.

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Hmm, as long as you don't always use the big cube as the baseline, that works.

There are still cases it won't work; in fact, sometimes the optimal packing is pretty strange. For example, check the fifth optimal square packing: https://en.wikipedia.org/wiki/Square_packing_in_a_square

Wow, that's a more bizarre case than I would have imagined. I started with the assumption that rotating them other than multiples of 90 degrees would never help, but looks like I was wrong.

Well to be fair, packing a physical good in that type of arrangement would often cause breakage of the diagonal object. So establishing flush edges seems like a good assumption here.

There's also an upper bound on how bad an axis-aligned solution can be. And, on a less mathematical note, weird diagonal packings are counter-intuitive to everyone and you're not likely to get customers complaining that you packed inefficiently just because you missed an opportunity to use one.

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