I think it is a shame people miss out on such good things, due to misunderstanding. The process I outlined in my post might seem like dry math, and it is, but it is the math of ideas, and can lead you to such beautiful places in your head and in your spirit. Discussions here in the Thoth forum might sound like code at times, very dry and intellectual, but they're actually about love and passion and spirit and basically life itself. The "code" is there simply to make sure everybody understands each other, since we are talking about emotions and experiences not easily expressed any other way. Attribution plus placement plus sign plus letter may sound dry, but it is very exciting because it forces you to bend your mind and spiritual senses to try to work out the answer to what do you get when you combine love with death with motion with perfection with, I don't know, whatever. And that process is just as intuitive and beautiful as anything. It makes you grow as a person, trying to arrive at the pure idea.
Plus there is the misconception that the images are not looked at. Nothing can be further from the truth. In the Thoth especially the images are so exactly engineered to convey the experience of the attributions, that the two go hand in hand. You not only know that, say, Mars is present on a card, but you feel it. Even if in a subtle way, it will be there, and will aid in your appreciation of the abstract energy depicted in the card.
Lastly, studying the structure helps make connections between the cards in ways that truly are practical in a reading. The three cards crossing the Abyss (Hierophant, Priestess and Chariot) are all connected astrologically, which not only leads to some mindblowing conclusions about each card's meaning, but also can hint to connections if they or any of the Minors or Courts associated with them come up. I have found that the amazing interconnectivity in the system has shown great insights in readings that looking at the images only would never have uncovered. It gives you a bigger vision, a bird's eye view since it can help you map out causes and effects of a situation. In addition, since every minor is two Majors, the reading itself becomes much bigger, and you have those added connections you can make. What does it mean if a planet or sign or letter repeat themselves? Do any Majors repeat themselves through attribution? These two cards here are next to each other on the Tree, is there significance? There really is no limit to how much practical use can be made of the structure. These two Courts share a sign, with it being more dominant it one of them, what do these two people have in common?
This is, of course, because the system is, with the exception of a few issues, so incredibly logical.