The problem is not so much with the systems in place at GIA, or AGS. It is also not so much a problem of the HCA. Diamonds are each individuals although we can make somewhat broad categories for them to assist people. We often end up creating confusion such as you are experiencing. Ultimately most Excellent cut GIA diamonds really do look very beautiful and will please nearly everyone. A person who gets and AGS 000 stone will undoubtedly think the diamond is lovely to look at, too. People who get a diamond with an HCA score as low as .8 certainly won't have a problem with the looks of their diamond. Each one of these system has variation of appearance, but they all are rather minor ones at the top category.
What we really can't agree upon, as an industry, is what "fine cut" really means. It currently means many different things to those of us who are involved. We more or less agree on some points, but market forces, competition and the fact that no governmental agency is in charge, stand in the way of clearly defining "fine cut" in diamonds. The sort of slight differences among diamonds at the top range of well cut are the kind of differences important to engineers, scientists and avid diamond fanatics, but of a lot less importance to romantics and appreciators of beauty. We just are not quite at the scientific level of grading we are striving to attain, but we sure know how to make pretty diamonds for many years already. Turning diamond grading into a science is swtrongly apposed by traditionalists of the diamond business. Many of these people and firms are hugely strong and financially powerful. What they don't want to happen generally does not happen. They apply pressure to the major labs to keep the status quo as it suits their traditional model. Since they are the primary clients of the labs, their financial clout is evident. Progress toward science based grading has been very slow, but it is not stagnant entirely.
Pricescope has become a huge force of change. Consumers, armed with facts, now pursue the diamonds they are looking for with power nearly matching the traditionalists. As the demographic of savvy consumers grows larger, you will see more labs converging on scientifically provable grading strategies. I see no possible outcome other than this, but I can't say when.
Try to find what it is about a diamond which you consider its beauty. Consider the cut grade as a part of the process since a well cut diamond is not only beautiful, but may be less damage prone than a less well cut diamond. A well cut diamond ought to look size appropriate for its weight, and not small for the weight. All of these considerations are part of what makes a fine diamond.
I hope you become less worried and also less confused.