When the crystal Gems were all in the forge, Bismuth calls Amethyst "Deep Cut." She says "Hey deep cut, what'chu packin'?"Then Amethyst pulls out her whip, Bismuth is actually impressed and continues, "Not every Quartz can make a whip like this."If you look up "Deep Cut" in gem termonology it says "When we discuess colored gemstones such as sapphire, ruby and emerald, the main motive of cut is to maximize color to its full potential. In contrast, cutting diamonds mostly refers to maximizing brilliance."
"Stones that are too deep will look smaller than expected but they will show off more color than they would if they were cut into normal proportions. Deep cut stones also preserve weight, increasing the cost of the stone without the expected increase in the size of the crown (top portion of the gem)."
We know why Amethyst is considered a defect by HomeWorld, she came out cut too deep, so she looks smaller. But check out what else it says about deep cut gems, their color is more saturated, vibrant, beautiful. That's why her her weapon is so special (or if the color has nothing to do with it, then a deeper cut would mean her potential is maxed out.) They also 'preserve weight' without having to be physically bigger. That could mean that Amethyst has more mass packed in her body than other gems, which could explain her shapeshifting prowess.
She used to shapeshift into Purple Puma for a long period of time before she had to rest and even shapeshifting into Jasper she could stay in that form for a long time. Remember how tired Steven got from just stretching his body a few inches. Her smaller body is also why she finally accepts herself. It takes her TEN SECONDSto reform after she was poofed the second time. It took Pearl TWO WEEKS. So in battle, Amethyst's small size gives her a tremendous advantage; she can literally save herself from being shattered by reforming almost immediately. No other gem has had that ability so far.
Finally, Amethys is just deep. She is a very deep person. "Stones that are too shallow will look big for their weight and appear lighter in color than deeper-cut stones." Why does that sound familiar? Jasper. Shallow has several meanings, her weapon is a helmet. Her battle strategy is to run into her foe. That is a shallow strategy. No one will stay with her because she only thinks of herself, she only sees things in her perspective, she lacs insight in other's emotions. She is in a way, shallow.
In conclusion. HomeWorld has a recourse problem, and Amethyst's deep cut gives her all the abilities of a regular cut quarts soldier plus more, while taking half the resources to create, and they'd consider her a defect? HomeWorld are fools.