Not everyone agrees that the best looking diamonds are the ones that score best on the HCA. For stones that are slightly less than perfect, the HCA may skew against a stone that the AGS skews towards.
The two scales aren't actually measuring the same things. The HCA is modeling a diamond, but it's very basic; no minor facets, no girdle, no crooked facets. AGS is actually modeling light shining through a diamond.
Adjustments to minor facets can make a diamond with relatively poor proportions look better. There is always a trade off, frequently loss of contrast.
Because the HCA has so many approximations, it's always less reliable than the cut score. But the cut score may not reflect your tastes. GIA excellent is a very broad score and while somebody likes every diamond, not everybody likes every diamond. HCA is narrower, but also much more likely to just be wrong.
Short answer:
AGS looks at an actual diamond's 57 facets and the angles between them.
HCA uses 4 numbers that are the result of the 57 facets and the angles between them.
If you play with the numbers on the HCA, you can see regions where HCA won't catch a diamond that gets an AGS 0 Cut.
What OP was asking is why a great AGS stone has a crappy HCA score, not the other way around, not why a great HCA score stone looks crappy.
I've read somewhere that you DON'T use HCA tool to check the AGS0 'cuz AGS0 trumps every HCA info.
Now, I don't know whether AGS0 is actually AGS tripple ideal or not.
BUT, not all AGS Ideal cut stones are equal. I have definitely seen a few I wouldn't consider buying. I do NOT use the HCA on AGS Ideal cut stones. They are already checked for light return. But, I would still not buy one without the images of the stone, because some are not as visually appealing as most of them.
Thanks all , I have an AGS ideal 0 stone and I love it. For fun, I put it in the HCA and it did not come out positive. But after some research, AGS ideal trumps and HCA tool and also the HCA tool can be very ambiguous .....